recursal/Fanatic-Fandom huggingface dataset:
The Galactic Mind

**The Galactic Mind** is an immensely powerful galactic level cosmic entity in the form of a giant galaxy-sized brain.

Within the Galactic Mind are billions upon billions of stars each containing their own brains which act as nodes in giant network of biological computers deep in outer space.

Furthermore, the galactic mind is able to link itself with other members of its species creating a ginormous cosmic mind which includes all the people and creatures in every galaxy throughout the universe's history.

Due to its nature as part of a hive mind, the galactic mind is made of pure information which means that it cannot be destroyed through conventional means under any circumstances.

It's main source of power comes from its ability to tap into vast amounts of information which it can then use to do such things as control the space-time continuum, negate temporal paradoxes, create life, control matter and energy, exist without a body, move entire galaxies with its mind, manipulate matter at the informational level and transfer its essence into anything its incomprehensible mind can find.
The Antibox

**The Antibox** is the cosmological object that is contained by everything. Regardless of internal properties, the Antibox is in it, for any value of "it".

In a sense, it is an opposite of the Box, though in a different one than an object that contains nothing (an empty set). Like the Box and other hypercosmological structures, the Antibox contains itself and is not wellfounded. As it is inside everything, it is, in a sense, an omnipresent object though it does not necessarily have other properties such as omnicapacity (which Box-equivalent structures have) or omnipotence (which the True God has).

Unlike the empty set, the definition of the Antibox given above does not automatically imply that it is a small object or even the smallest object containmentwise. The Antibox is still completely capable of containing objects, it would just be also contained within those objects. Of course, one can take the Antibox to be an object that does not contain any other objects within it (other than itself) and consider it to be very small—the definition of the Antibox does not state anything about any other objects and their relation to the Antibox so it is reasonable to assume so. Equally, it is also reasonable to assume that there are other non-Antibox things inside the Antibox. One interesting case would be a Box-equivalent structure.

## Positions on Scales

On a surreal verse level system that uses the class of affinely extended surreal numbers rather than the class of projectively extended surreal numbers, one that considers the Antibox to be minimal can place the Antibox at

−
∞

{\displaystyle -\infty }

, the affine infinity less than all surreal numbers, while the Box is at

∞

{\displaystyle +\infty }

. This is to ensure that the Antibox has the smallest index and the Box has the largest index and that the former is contained by and the latter contains everything regardless of how simple or complicated any indexed structure is (the birthday of the surreal number doesn't matter,

−
∞

{\displaystyle -\infty }

 and

∞

{\displaystyle +\infty }

).

On Holomanga's Unreality Scale, the Antibox can be considered to have an equal "unreality" with the Box. This places it at the projective

∞

{\displaystyle \infty}

 in the class of projectively extended surreal numbers.
Reference Field

The Reference field is a cosmology which is defined by a relaxation of the definition of the Schemafield and may be Box equivalent. Every object with a property describable in any language, format, or media is in the Reference field, including the Box. For example, the empty set is in the Reference field simply due to the fact it can be represented as "{}" in set notation. The Reference field is different from the Schemafield, in that it contains everything with a property, not every set of things with a property. If the Reference field is indeed Box equivalent, that means that all objects with properties are cosmologies.
Spiral arm

A **spiral arm** is a region of a galaxy made of relatively densely-packed stars and interstellar gas and dust, in a curved formation caused by the movement of density waves. Stars move in and out of spiral arms; the most common way to explain this is like a traffic jam, where cars will enter and leave but the jam persists.

Spiral galaxies, barred spiral galaxies, and irregular spiral galaxies (to some extent) have spiral arms or arm-like structures. Most galaxies have only a few; the Milky Way is thought to have four main arms plus some number of minor ones.
Polyverse

The polyverse is the source of every opposite thing in existence, where the polarity of all things originate (according to Holomanga's cosmology, it may contain an infinite amount of Godverses and Omniverses).

## History

It is possible that the Polyverse was before the Omniverse itself. When the omniverse was created (if it was created), the exact opposite of the omniverse may have also been created, if so then this may have been done within the polyverse.

This could also mean the polyverse was simply a verse among other separate verses that were eventually brought together in the omniverse.
Split-complex line

The **split-complex line** is a space created from considering all points that can be labeled with one split-complex number, numbers similar to complex numbers but the imaginary unit is a solution to the square root of +1 rather than -1. This gives it one split-complex dimension, and two real dimensions.

The split-complex line is isomorphic to the real plane and multiplication of split-complex numbers on the unit hyperbola can represent Lorentz transformations of a Minkowski plane akin to how the complex line is isomorphic to the real plane and multiplication of complex numbers on the unit circle can represent rotations of the Euclidean plane.
Square-pentagonal duoprism

A **square-pentagonal duoprism** is the shape created from the Cartesian product of a square and a pentagon.

Its Bowers acronym is **squipdip**.

## See Also

t

0
,
2

{
4
,
2
,
3
}

{\displaystyle t\_{0,2} \{4,2,3\}}

t

0
,
2

{
4
,
2
,
4
}

{\displaystyle t\_{0,2} \{4,2,4\}}

t

0
,
2

{
4
,
2
,
5
}

{\displaystyle t\_{0,2} \{4,2,5\}}

t

0
,
2

{
4
,
2
,
6
}

{\displaystyle t\_{0,2} \{4,2,6\}}

t

0
,
2

{
4
,
2
,
7
}

{\displaystyle t\_{0, 2} \{4, 2, 7\}}

t

0
,
2

{
4
,
2
,
8
}

{\displaystyle t\_{0,2} \{4,2,8\}}

Template:Variant Nav t02 X 2 5
Planck time

The **Planck time** (tP) is the characteristic timescale of Planck units. Planck time is most easily defined as the time required for light to travel in a vacuum a distance of 1 Planck length, and is approximately 5.39 × 10−44 s.

## Derivation

The simplest derivation comes from considering the Planck length

ℏ
G

c
3

{\displaystyle \sqrt{\frac{\hbar G}{c^3}}}

. Since length is the product of velocity and time, the Planck time can be obtained by dividing by the speed of light (the Planck velocity), to get

ℏ
G

c
5

{\displaystyle \sqrt{\frac{\hbar G}{c^5}}}

.
Point triplet

A **point triplet**, also known as the **discrete space of three points**, is a shape made up of three disconnected points. It can be thought of as the vertices of a triangle.

Its most natural embedding is in two dimensions, where the three points make up the vertices of a triangle, but it also has a one-dimensional embedding as three points in a line. It can be considered as a subset of the real line with the subspace topology comprising three disconnected elements (for example, {0, 1, 2}).
Teraverse

The **Teraverse** is the fifth nested level of the metric -verse series and the second lowest-level archverse. This -verse contains a finite or infinite

amount of gigaverses, which are the fourth nested level. It is contained by the Petaverse, which is an finite or infinite set of teraverses.

At the scale of Teraverse, the dimensionality becomes hard to measure. Like a Gigaverse this is caused by the fractal nature of a Teraverse. The dimensionality of the common teraverse are most likely to be 11-Dimensional to 14-Dimensional. Higher Archverses will definitly have more dimensions, but its impossible to know how many.
Pentagon

A **pentagon** is a 2-dimensional polygon with five edges. The Bowers acronym for a pentagon is **peg**. It is called a **cosmogon**, **hydrogon**, or a **rhodogon** under the elemental naming scheme.

## Structure and Sections

The regular pentagon has equal edges and each angle being 108 degrees.

### Hypervolumes

* vertex count =

5

{\displaystyle 5}
* edge length =

5
l

{\displaystyle 5l}
* surface area =

5
(
5
2

5

)

4

l

2

{\displaystyle {\frac {\sqrt {5(5+2{\sqrt {5}})}}{4}}{l}^{2}}

### Subfacets

* 1 null polytope (-1D)
* 5 points (0D)
* 5 line segments (1D)
* 1 **pentagon** (2D)

### Radii

* Vertex radius:

5

5

10

l

{\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{10}}}l}
* Edge radius:

5
2

5

5

2

l

{\displaystyle {\frac {{\sqrt {\frac {5+2{\sqrt {5}}}{5}}}{2}}{l}}}

### Vertex coordinates

The coordinates of a pentagon in the plane are:

* (0,√((10+2√5)/5)
* (±(1+√5)/2,√((5-√5)/10)
* (±1,-√((5+2√5)/5)

### Related shapes

* Dual: Self-dual
* Vertex figure: Line segment, length φ =

1

5

2

{\displaystyle \frac{1+\sqrt{5}}{2}}
* Conjugate: Pentagram

## See Also

t
0

{
5
}

{\displaystyle t\_0 \{5\}}

t
1

{
5
}

{\displaystyle t\_1 \{5\}}

t

0
,
1

{
5
}

{\displaystyle t\_{0,1} \{5\}}
Polychoron

A **polychoron** (/ˌpälēˈkôrən/ or /ˌpälēˈkôrän/), plural *polychora,* is a 4-dimensional polytope composed of points, line segments, faces, cells, and a single teron, all of which are polytopes. Polychora can be considered subsets of a Euclidean flune.

Polychora make up the boundary of 5D polytera and define their surteron bulk.

## Uniform polychora

A uniform polychoron is a polychoron that are vertex-transitive and bound by uniform facets. Each face is a regular polygon and each cell is a uniform polyhedron. As of January 2024, there are 2191 known uniform polychora (excluding the infinite duoprism and antiduoprism families), most of which were discovered by the two amateur mathematicians Jonathan Bowers and George Olshevsky. Uniform polychora whose cells are all congruent and angles are all equal are known as **regular polychora**. All regular polychora have a three-entry Schläfli symbol.

There are sixteen regular polychora, six convex and ten star polychora (known as the **Schläfli-Hess polytopes**).

The six regular convex polychora are the pentachoron (**pen**), the tesseract (**tes**), the hexadecachoron (**hex**), the icositetrachoron (**ico**), the hecatonicosachoron (**hi**), and the hexacosichoron (**ex**).

The ten regular star polychora are the faceted hexacosichoron (**fix**), the great hecatonicosachoron (**gohi**), the grand hecatonicosachoron (**gahi**), the small stellated hecatonicosachoron (**sishi**), the great grand hecatonicosachoron (**gaghi**), the great stellated hecatonicosachoron (**gishi**), the grand stellated hecatonicosachoron (**gashi**), the great faceted hexacosichoron (**gofix**), the grand hexacosichoron (**gax**), and the great grand stellated hecatonicosachoron (**gogishi**).

## References

* https://en.wikipedia.org/wiki/4-polytope
* http://www.polytope.net/hedrondude/polychora.htm
Pentagonal cupola

The **pentagonal cupola** is a three-dimensional polyhedron constructed as a cupola with a pentagon at the top, making it a segmentohedron with bases of a decagon and a pentagon. It is the fifth Johnson solid.

## Structure and Sections

### Subfacets

* 15 points (0D)
* 25 line segments (1D)
* 5 triangles (2D)
* 5 squares (2D)
* 1 pentagon (2D)
* 1 decagon (2D)
* 1 pentagonal cupola (3D)

## See Also

{
2
}

t

0
,
1

{
2
}

{\displaystyle \{ 2 \} \vert \vert t\_{0,1} \{ 2 \} }

{
3
}

t

0
,
1

{
3
}

{\displaystyle \{ 3 \} \vert \vert t\_{0,1} \{ 3 \} }

{
4
}

t

0
,
1

{
4
}

{\displaystyle \{ 4 \} \vert \vert t\_{0,1} \{ 4 \} }

{
5
}

t

0
,
1

{
5
}

{\displaystyle \{ 5 \} \vert \vert t\_{0,1} \{ 5 \} }

{
6
}

t

0
,
1

{
6
}

{\displaystyle \{ 6 \} \vert \vert t\_{0,1} \{ 6 \} }
Solid quadruple torus

A **solid double torus** is the three-dimensional surcell bounded by a quadruple torus. This means that, in its usual embedding, it makes up the solid interior of the quadruple torus.

## Structure and Sections

### Subfacets

* 1 quadruple torus (2D)
* 1 solid quadruple torus (3D)

## See Also

S

2

{\displaystyle \mathbb S^{2}}

T

2

{\displaystyle \mathbb{T}^2}

2

T

2

{\displaystyle 2\mathbb{T}^2}

3

T

2

{\displaystyle 3\mathbb{T}^2}

4

T

2

{\displaystyle 4\mathbb{T}^2}
Rectification

**Rectificiation** is a shape operation in which the midpoints of all of the edges of a polytope are marked, and then the vertices are cut off at those points. This creates a new shape bounded by facets that are the vertex figures of the old one, as well as the recified forms of the existing facets.

For example, a cube, with triangular vertex figures and square faces, becomes a cuboctahedron, with triangular and square faces, when rectified.

If a shape is defined with a linear Coxeter-Dynkin diagram, the recitifed form can be found by ringing only the second node. This means that a rectification can be represented with the Schläfli symbol operator

t
1

{\displaystyle t\_1}

.

## References

1. ↑ https://web.archive.org/web/20070207021813/http://members.aol.com/Polycell/glossary.html#Rectification
Spherinder

A **spherinder** is a four-dimensional rotatope produced by the product of a line segment and a ball; this means that it is a prism with a ball as the base. It is composed of two balls and a curved 3-D surface, similar to how a 3-D cylinder is composed of two discs and a curved 2-D surface.

## Structure and Sections

The spherinder has two types of sections. It can either be an unchanging ball or a line segment expanding to a cylinder before shrinking back.

### Subfacets

* 2 spheres (2D)
* 2 balls (3D)
* 1 spheritube (3D)
* 1 spherinder (4D)
Rift turbine

A **rift turbine** is an engine bearing some similarities to a classical warp drive, but designed solely for travel through the otherwise non-navigable Rifters' Realm. Every Realm-capable vehicle mounts a rift turbine, though they can be of varying sizes: tiny "pods" meant for quick jumps between universes have turbines no larger than a human arm, while the greatest of vessels mount turbines of inconceivable sizes well past the megaparsecs in length.

## Functionality

A rift turbine is cylindrical in shape, mounting a spatial motor on each end - each one similar to a traditional jet turbine, though designed to remove a point in space from inside the cylinder. To operate, the cylinder creates a power imbalance by stretching the point into a line segment and thus forcing the spacial motors to attempt to collapse the segment from the forward end first.

As the point is "supposed" to be anchored to the interior of the cylinder but disconnected from the Realm outside, this effect causes the entire vehicle to shift forwards every time the line segment contracts, generating singularities in nearby points as the local space attempts to catch up.

In order to turn, Realm-capable vehicles mount smaller rotational turbines at angles along their sides, and then simply switch to them, as only one can run at a time.

## SICO

As the speed of travel is dependent on both the line segment's maximum length and the speed of its oscillation - both of which are arbitrary given the constant correction factors involved - it is rarely useful to compare speed with either of these. Thus, speed is instead given by the strength of the singularities generated by the turbine as the vehicle moves: the singularity induction coefficient, or the SICO.

A SICO of 0 loosely corresponds to a forward speed of one parsec per second, and each integer above or below this equates to a difference of roughly one order of magnitude.
Portal

A **portal** is a temporary or permanent hole in two locations that connects those two points, this can occur in space, interstellar space, intergalactic space, or even in different universes, so that they are physically adjacent, at least in a way. Portals can take many sizes; some might be so small that even single quarks cannot fit through, while others might span entire galaxy clusters. They can be of many colors, shapes, and functionalities; portals might have mass limitations restricting certain amounts of travel through them, or have a delay between entering one side and exiting the other.

Advanced civilizations might be able to achieve high enough energy densities to create portals on their own. Powerful beings can create portals easily.
Pataverse

## Size

### Dimensionality

Usually the same number as the host sentient being, due to natural limits on imagination

A **pataverse** is a type of unstable -verse, partially related to virtual spaces such as metaverses or hyperverses, and sharing many features with Internal Reality, that is created through a sentient being's imagination rather than sheer processing power.

Pataverses are inherently ill-defined due to their nature; it is difficult, and often impossible, for a typical sentient to imagine the entire contents of one universe down to the particle level, so anything not imagined is "filled in" by a network of unstable laws of physics and logic. Such a phenomenon is a powerful and dangerous form of the multiversal process of blurring.

A pataverse ends when its host sentient being stops imagining it. However, from within the pataverse, this may take an infinite amount of subjective time.

They are the standard cosmology equivalent to an Imaginata. They also match the type of imaginatas that can exist in areas of the Imaginarium that are limited by information theory.
Staticverse

A **staticverse** is a universe with chaotic laws of physics, leading to most of the universe being entirely unpredictable. All physical properties in a staticverse vary rapidly and randomly. This means that, to an observer looking at a staticverse, it resembles TV static or white noise, with nothing complicated arising except by chance and for limited periods of time. In the most extreme cases even space and time would not exist in a consistent form and would also be part of the static.

Any life in a staticverse, if present, would have to be ephemeral and most likely of the form of Boltzmann brains. Producing complicated thoughts would be very difficult, however, as these would immediately vanish into the static.
Quantum

A **quantum** is a discrete unit of energy proportional in magnitude to the frequency of the radiation it represents. Quantumunits of energy prevent the electron in an atom from spiraling towards the center, as in order to fall the electron must lose a fractional amount of energy, and quantum are whole numbers, therefore the electron cannot collapse to the atom's center.
Ridge

In higher-dimensional geometry, the **ridges** are the (*n*-2)-subfacets of any *n*-polytope. A ridge is seen as the boundary between exactly two facets of a polytope or honeycomb. The ridges of a polytope should always be the contact region of two facets, otherwise it is an exotic polytope.

For example:

* The ridges of a 1D polytelon are null.
* The ridges of a 2D polygon or 1D tiling are its 0-faces or vertices.
* The ridges of a 3D polyhedron or plane tiling are its 1-faces or edges.
* The ridges of a 4D polychoron or 3-honeycomb are its 2-faces or simply **faces**.
* The ridges of a 5D polyteron or 4-honeycomb are its 3-faces or cells.

## See also

...Spire · Peak · **Ridge** · Facet · Polytope
Tetracomtelon

A **tetracomtelon** is a complex 1-dimensional polytope of 4 points on a complex line. These points have no natural ordering, so no interior can be defined. They can be represented as a square embedded in the complex line.

## References

1. ↑ https://en.wikipedia.org/wiki/Complex\_polytope#Regular\_complex\_one-dimensional\_polytopes

## See Also

{
}

{\displaystyle \{\}}

3

{
}

{\displaystyle \_3\{\}}

4

{
}

{\displaystyle \_4\{\}}

5

{
}

{\displaystyle \_5\{\}}

6

{
}

{\displaystyle \_6\{\}}
Penteract

A 5-D equivalent to the Rubik's Cube, a 3x3x3x3x3.

A **penteract** or **decateron** is the 5 dimensional hypercube. Its bowers acronym is **pent**. It is also called a **geoteron**. It can be considered to be a prism with a tesseract as the base.

Penteractic Rubik's cubes can found online, but cannot be built in our world of limitations.

## Structure and Sections

The penteract is a tesseractic prism, and its main section sequence is an unchanging tesseract.

### Hypervolumes

* vertex count =

32

{\displaystyle 32}
* edge length =

80
l

{\displaystyle 80l}
* surface area =

80

l

2

{\displaystyle 80{ l }^{ 2 }}
* surcell volume =

40

l

3

{\displaystyle 40{ l }^{ 3 }}
* surteron bulk =

10

l

4

{\displaystyle 10{ l }^{ 4 }}
* surpeton pentavolume =

l

5

{\displaystyle { l }^{ 5 }}

### Subfacets

* 32 points (0D)
* 80 line segments (1D)
* 80 squares (2D)
* 40 cubes (3D)
* 10 tesseracts (4D)
* 1 penteract (5D)

## See Also

**Pentacross facetings:** hehad · phap · nophap
**Demipenteract regiment:** hin · dah · han · radah · rinah · hit

{
2
,
3
,
3
,
3
}

{\displaystyle \{2,3,3,3\}}

{
3
,
3
,
3
,
3
}

{\displaystyle \{3,3,3,3\}}

{
4
,
3
,
3
,
3
}

{\displaystyle \{4,3,3,3\}}

{
5
,
3
,
3
,
3
}

{\displaystyle \{5, 3, 3, 3\}}

{
4
,
3
,
3
,
2
}

{\displaystyle \{4,3,3,2\}}

{
4
,
3
,
3
,
3
}

{\displaystyle \{4,3,3,3\}}

{
4
,
3
,
3
,
4
}

{\displaystyle \{4,3,3,4\}}

{
4
,
3
,
3
,
5
}

{\displaystyle \{4,3,3,5\}}

Template:Variant Nav 4 3 3 3
Regiment

A **regiment** is a group of polytopes that share edge arrangements. The most convex representative of a regiment is called a **colonel**, with it's conjugate being called the **lieutenant**. A regiment is named after it's colonel (for example, the icosahedron regiment is named after the icosahedron because it is the most convex of the members, which consist of the colonel and the great dodecahedron).

## References

1. ↑ https://web.archive.org/web/20070207021813/http://members.aol.com:80/Polycell/glossary.html#Regiment
Truncation

**Truncation** is a shape operation that intuitively, chops off all the corners of a polytope and exposes all of the polytope's vertex figures. Truncation replaces all vertices with their vertex figures and all facets with their truncated versions. For example, truncating a cube, which has square faces and triangular verfs, will give out a shape whose faces are truncated squares and triangles. Truncating a polygon

{
p
}

{\displaystyle \{p\}}

 will give out a polygon with symbol

{
2
p
}

{\displaystyle \{2p\}}

.

Generally when truncating a uniform polytope, the **uniform truncation** is considered. The uniform truncation of a polytope is the truncated polytope such that all of its facets are uniform. Uniform truncation is represented by ringing the first and second nodes of the Coxeter diagram. Uniform truncation can be represented with the Schläfli symbol operator

t

0
,
1

{\displaystyle t\_{0,1}}

.

## References

1. ↑ https://web.archive.org/web/20070207021813/http://members.aol.com/Polycell/glossary.html#Truncation
Purgatory

**Purgatory** is the temporary state in the afterlife. The soul of a person who has not been purified in their lifetime is sent here to do so.

There is also the view that purgatory can just be the state of mind felt by spirits that where neither truly good nor considerably evil either, living in the Spirit World, trying to learn some final license or purifying themselves by cleansing their conscience from the lingering guilt of some less elevated actions. In that sense it would be just a type of Internal Reality.
Rhombicuboctahedron

A **rhombicuboctahedron** is a uniform three-dimensional polyhedron that can be constructed by cantellating a cube or octahedron

As a cantellated octahedron, it has the same symmetry group as the octahedron, namely octahedral symmetry (Oh).

The dual of the cuboctahedron is called a deltoidal icositetrahedron.

The Bowers acronym for the cuboctahedron is **sirco**.

## Structure and Sections

On each vertex of the cuboctahedron, one triangle and three squares join.

## See Also

t
0

{
4
,
3
}

{\displaystyle t\_0 \{4,3\}}

t
1

{
4
,
3
}

{\displaystyle t\_1 \{4,3\}}

t
2

{
4
,
3
}

{\displaystyle t\_2 \{4,3\}}

t

0
,
1

{
4
,
3
}

{\displaystyle t\_{0,1} \{4,3\}}

t

1
,
2

{
4
,
3
}

{\displaystyle t\_{1,2} \{4,3\}}

t

0
,
2

{
4
,
3
}

{\displaystyle t\_{0,2} \{4,3\}}

t

0
,
1
,
2

{
4
,
3
}

{\displaystyle t\_{0,1,2} \{4,3\}}

t
0

{
3
,
3
}

{\displaystyle t\_0 \{3,3\}}

t
1

{
3
,
3
}

{\displaystyle t\_1 \{3,3\}}

t
2

{
3
,
3
}

{\displaystyle t\_2 \{3,3\}}

t

0
,
1

{
3
,
3
}

{\displaystyle t\_{0,1} \{3,3\}}

t

1
,
2

{
3
,
3
}

{\displaystyle t\_{1,2} \{3,3\}}

t

0
,
2

{
3
,
3
}

{\displaystyle t\_{0,2} \{3,3\}}

t

0
,
1
,
2

{
3
,
3
}

{\displaystyle t\_{0,1,2} \{3,3\}}

Template:Variant Nav t02 4 X
Template:Variant Nav t02 X 4

t

0
,
2

{
2
,
3
}

{\displaystyle t\_{0,2} \{2,3\}}

t

0
,
2

{
3
,
3
}

{\displaystyle t\_{0,2} \{3,3\}}

t

0
,
2

{
4
,
3
}

{\displaystyle t\_{0,2} \{4,3\}}

t

0
,
2

{
5
,
3
}

{\displaystyle t\_{0,2} \{5,3\}}

t

0
,
2

{
6
,
3
}

{\displaystyle t\_{0,2} \{6,3\}}

t

0
,
2

{
7
,
3
}

{\displaystyle t\_{0,2} \{7,3\}}

t

0
,
2

{
8
,
3
}

{\displaystyle t\_{0,2} \{8,3\}}

t

0
,
2

{
∞
,
3
}

{\displaystyle t\_{0,2} \{\infty,3\}}

t

0
,
2

{

π
i

λ

,
3
}

{\displaystyle t\_{0,2} \{\frac{\pi i}{\lambda},3\}}

Template:Variant Nav t02 3 X
Pentasphere

A **pentasphere** is a 5-dimensional surface produced by finding the set of all points that are an equal distance from another point in 6-dimensional space. Because it is curved, it is often represented embedded in 6-dimensional space. A pentasphere is the shape of the exterior of a hexorb. It is the 5-dimensional hypersphere.
Standard model

The **standard model** of contemporary physics is a way of describing the essence and interaction of 17 fundamental particles (alternatively *waves*, given quantum mechanical duality). Through these 17 particles it is believed the universe and most of the fundamental forces operate.

## Types

In the standard model there are two basic types of particles: *Fermions* and *Bosons*. Fermions are like milk jugs while bosons are like milk trucks. Just as the milk truck goes up and down the lane to transfer bottles of refreshing liquid to thirsty customers, so too bosons mediate, or moderate, interaction between the fermions, or bits of matter, which are like houses. The Bosons and the forces or properties they mediate are as follows:

* Gluon - Strong nuclear force
* Photon - Electromagnetic force
* W & Z Bosons - Weak nuclear force
* Higgs Boson - Mass

Gravity is unaccounted for in the standard model, though a hypothesized mediator of the force dubbed the *graviton* exists in theory.

The fermions themselves consist of six *quarks* and six *leptons*. The two quarks Up and Down make up most of observable matter, with the four additional 'flavors'; Strange, Charm, Top, and Bottom being responsible for exotic forms of matter. The leptons are associated with less tangible substance but are still highly influential in particle physics, the most prominent of them being the *electron*. There is also the muon, tau, and the "evil nuetrino twin" counterpart of these three leptons, named the electron neutrino, muon neutrino, and tau nuetrino.
Spiral galaxy

**Spiral galaxies** are a type of galaxy that are disc-like in shape but have their disc of stars spun into a set of spiral arms where there is a higher concentration of nebulae and large, bright stars. It is believed that stars will regularly "pile up" inside these arms like a traffic jam, and then leave the arm to travel to the next one. Like elliptical galaxies, they vary in size from millions of stars to trillions.

Spiral galaxies can be subdivided from Sa to Sd, with later letters indicating a looser and more diffuse spiral. The Sa subcategory is usually reserved for the tightest galaxies, with Sd being the most diffuse.

Well-known spiral galaxies in our universe include M33, the Pinwheel Galaxy, the Andromeda Galaxy, and the Milky Way.
Power

**Power** is the rate of change of energy.

The dimensions of power are [mass][length]2[time]-3.

## Calculation

Instantaneous power P can be calculated by taking the time derivative of energy E through

# P

d
E

d
t

{\displaystyle P = \frac{dE}{dt}}

.

## Kardashev Scale

The Kardashev scale is one way of categorising civilisations by their total power output. Each additional level on the Kardashev scale represents an increase in power output of a factor of 10 billion.

* Type 1.0 - 1016 watts
* Type 2.0 - 1026 watts
* Type 3.0 - 1036 watts
* Type 4.0 - 1046 watts
* Type 5.0 - 1056 watts
Square cupola

The **square cupola** is a 3-Dimensional polyhedron constructed as a cupola with a square as the top, making it a segmentohedron with bases of a square and an octagon. It can also be seen as a slice of a rhombicuboctahedron. It is the fourth Johnson solid.

Its Bowers acronym is **squacu**.

## Structure and Sections

### Subfacets

* 12 points (0D)
* 20 line segments (1D)
* 4 triangles (2D)
* 5 squares (2D)
* 1 octagon (2D)
* 1 square cupola (3D)

### Hypervolumes

* vertex count =

9

{\displaystyle 9}
* edge length =

15
l

{\displaystyle 15l}
* surface area =

(

7
2

2

3

3

)

l
2

{\displaystyle \left(7 + 2\sqrt{2} + 3\sqrt{3} \right) l^2}
* surcell volume =

(

1

2

2

3

)

l
3

{\displaystyle \left( 1 + \frac{2 \sqrt{2} }{3} \right) l^3}

## See Also

{
2
}

t

0
,
1

{
2
}

{\displaystyle \{ 2 \} \vert \vert t\_{0,1} \{ 2 \} }

{
3
}

t

0
,
1

{
3
}

{\displaystyle \{ 3 \} \vert \vert t\_{0,1} \{ 3 \} }

{
4
}

t

0
,
1

{
4
}

{\displaystyle \{ 4 \} \vert \vert t\_{0,1} \{ 4 \} }

{
5
}

t

0
,
1

{
5
}

{\displaystyle \{ 5 \} \vert \vert t\_{0,1} \{ 5 \} }

{
6
}

t

0
,
1

{
6
}

{\displaystyle \{ 6 \} \vert \vert t\_{0,1} \{ 6 \} }
Square dihedron

A **square dihedron** is a 3-D polyhedron with two square faces which share their edges and vertices. In normal Euclidean space, it is degenerate, but can exist as a tiling of the sphere where each face makes up a hemisphere.

## See Also

{
4
,
2
}

{\displaystyle \{4,2\}}

{
4
,
3
}

{\displaystyle \{4,3\}}

{
4
,
4
}

{\displaystyle \{4,4\}}

{
4
,
5
}

{\displaystyle \{4,5\}}

{
4
,
6
}

{\displaystyle \{4,6\}}

{
4
,
7
}

{\displaystyle \{4,7\}}

{
4
,
8
}

{\displaystyle \{4,8\}}

{
4
,
∞
}

{\displaystyle \{4,\infty\}}

{
4
,

π
i

λ

}

{\displaystyle \{4, \frac{\pi i}{\lambda}\}}

t
0

{
4
,
2
}

{\displaystyle t\_0 \{4,2\}}

t
1

{
4
,
2
}

{\displaystyle t\_1 \{4,2\}}

t
2

{
4
,
2
}

{\displaystyle t\_2 \{4,2\}}

t

0
,
1

{
4
,
2
}

{\displaystyle t\_{0,1}\{4,2\}}

t

1
,
2

{
4
,
2
}

{\displaystyle t\_{1,2} \{4,2\}}

t

0
,
2

{
4
,
2
}

{\displaystyle t\_{0,2} \{4,2\}}

t

0
,
1
,
2

{
4
,
2
}

{\displaystyle t\_{0,1,2} \{4,2\}}

{
0
,
2
}

{\displaystyle \{0,2\}}

{
1
,
2
}

{\displaystyle \{1,2\}}

{
2
,
2
}

{\displaystyle \{2,2\}}

{
3
,
2
}

{\displaystyle \{3,2\}}

{
4
,
2
}

{\displaystyle \{4,2\}}

{
5
,
2
}

{\displaystyle \{5,2\}}

{
6
,
2
}

{\displaystyle \{6,2\}}

{
7
,
2
}

{\displaystyle \{7,2\}}

{
8
,
2
}

{\displaystyle \{8,2\}}

{
∞
,
2
}

{\displaystyle \{\infty,2\}}

{

π
i

λ

,
2
}

{\displaystyle \{\frac{\pi i}{\lambda},2\}}
Pentrealmverse

A **pentrealmverse** is a universe that occupies 5-Dimensional Space.

As usual, pentrealmverses may have one or more temporal dimensions, or theoretically none - but a universe without time is a universe without an origin, which violates causality and is generally not permissible within the confines of low-level -verses like multiverses or megaverses.
The Absolute Ghost

The **Absolute Ghost** is an entity who managed to go through absolute death and re-enter the Omniverse.

## Origin

The Absolute Ghost was an archversal entity who was approached by the Dealer in a game. However, the Absolute Ghost was wary of a seemingly normal three-dimensional being challenging a being of their caliber to a game and decided to kill the Dealer instead. This is not an uncommon occurrence and usually, this resulted in the Dealer using one of his readily available cards to disarm the other party. However, the conditions were exactly right for the Dealer to give absolute death to the Absolute Ghost. Firstly, several effects given by the cards the Dealer had were wearing off and he couldn't pick a card with precision. Secondly, a card that gave absolute death happened to be the closest card that could disarm the Absolute Ghost. The Absolute Ghost was killed in such a way that they exited the Omniverse entirely. Nobody remembered them except for the Dealer, and perhaps users of high magic, such as Odhin. They wandered around the Outside until somehow they managed to enter the Omniverse. This shouldn't have been possible without intervention from beings inside the Omniverse who knew of their existence, or Creator, Destroyer, and other beings of their caliber's intervention, but somehow it happened. Not even Omniversal Travelers could enter the Omniverse from absolute death. Thus, the Absolute Ghost gained their name, as well as infamy, for being the only entity to be resurrected from absolute death without intervention from beings within the Omniverse.

## Abilities

Due to the Absolute Ghost's nature as a ghost of one killed by absolute death, many believe the Absolute Ghost to be immortal, for the fact that, as a ghost, they are impossible to kill except by being sent into the Outside again. One of the Absolute Ghost's most notable powers is their ability to nullify magic entirely, though they have little control over their power. This has attracted attention from various entities who wish to harness the Absolute Ghost's power.

## Enemies

The Absolute Ghost, being a survivor of absolute death, is targeted by various groups, many of which, the Absolute Ghost considers enemies. In other cases, the Absolute Ghost makes enemies, from a need to simply be safe.

The Odhinites want to capture them to research anti-magical phenomena.

The Mevalkagna are worried that the Absolute Ghost's abilities can cause Omniversal plurality, however, the Absolute Ghost does not seem interested in building an empire, but rather simply safety from other entities who want to take their power.

The Dealer is considered an enemy by the Absolute Ghost, being the reason they are suffering, as well as the fact that they consider the Dealer to be a threat to their safety.
Petaverse

The **Petaverse** is the sixth nested level of the metric -verse series and the third lowest-level archverse. This -verse contains a finite or infinite amount

## Position

### Contents

Teraverse

of teraverses, which are the fifth nested level. It is contained by the Exaverse, which is an finite or infinite set of petaverses.

The Petavere density depends on the region. the center of the Petaverse is the densest, wich is noticeable by its bright blue color. the outer regions are the least dense.
Riemann surface

f(z) = sqrt(z)

A **Riemann surface** is a 1-Dimensional connected complex manifold. that can informally Informally, it can be described as a "deformed" version of the complex line. Every point on a Riemann surface has a neighbourhood homeomorphic to an open disk in the complex line, but Riemann surfaces can have completely different global topologies than that of the complex line's. Examples of Riemann surfaces include the complex line, the Riemann sphere and spheres and tori created from the complex line.

Riemann surfaces are very important to complex analysis as they can be used to represent complex-valued holomorphic functions and can be used to study their behaviour, particularly those of multivalued functions such as exponentiation, roots, logarithms and inverse trigonometric functions.

The images show the projection of the Riemann surfaces of well-known functions from the complex plane to a 3-dimensional space, showing the real part of the output (imaginary part for ln(z)) and the colour representing the argument.

## Gallery

f(z) = cbrt(z)f(z) = ln(z)f(z) = arcsin(z)
Subgiant

A **subgiant** is a type of star with a luminosity (and generally size) in between that of a main sequence star and that of a giant star. Subgiants fuse hydrogen in a shell near their outer layers, as they have depleted all of the hydrogen at their cores. On an H-R diagram, the subgiant branch is visible as a bent stripe slightly above the main sequence.

Low-mass stars do not develop into subgiants, but more massive stars spend varying amounts of time at this stage; generally, the more massive the star, the quicker it passes through the subgiant stage. After this, stars evolve into giants or supergiants.

**Brown dwarf classes**: **Y** · **T** · **L** · **M**
**Wolf-Rayet and carbon star classes**: **S** · **C** · **W**
**Stellar remnant classes**: **D** · **N** · **Ω**

## References

1. ↑ https://en.wikipedia.org/wiki/Subgiant
Galacticity

**Galacticity** is a category of sentience corresponding to an information processing rate of 1042 bits/sec (a sentience quotient of 40-50 for a 100 kg individual). Galactic sentient individuals are able to innately understand the workings of an entire galactic civilisation of typical conscious beings. This means that a single galactic sentient individual could easily run a Type 3.0 Civilization alone, or multiple could form a Type 4.0 Civilization from many integrated galactic cultures.

## References

* http://www.xenology.info/Xeno/25.2.2.htm
Quasitruncated great stellated dodecahedron

A **quasitruncated great stellated dodecahedron** is a uniform polyhedron with 20 triangular faces and 12 decagrammic faces.

Its Bowers acronym is **quit gissid**.

## Structure and Sections

### Subfacets

* 32 points (0D)
* 90 line segments (1D)
* 20 triangles (2D)
* 12 decagrams (2D)
* 1 quasitruncated great stellated dodecahedron (3D)

## See Also

* Polytope Wiki. "Quasitruncated great stellated dodecahedron".
* Bowers, Jonathan. "Polyhedron Category 2: Truncates".
Supercluster

A **supercluster** is a large assembly of thousands or tens of thousands of galaxies which form some of the largest-scale structures in our universe. They contain smaller groups called galaxy clusters and galaxy groups, which together contain galaxies of every type - it's very common to see lots of elliptical and spiral galaxies together in a supercluster.

Normally, superclusters are the largest structures in the universe which are gravitationally bound. Many superclusters have enough mass to keep themselves together against the accelerating force of dark energy.
Wavefunction

In quantum mechanics, the **wavefunction** of a system, often denoted

Ψ

{\displaystyle \Psi}

, is a function of time that gives the state of the system. The wavefunction exists as a point in the infinite-dimensional Hilbert space of all possible states of the system. By writing the wavefunction as a sum of eigenstates of an operator, it is said to be in the representation of that operator, such as the position representation or the energy representation.

When written out as a sum of eigenstates, the amplitude of observing a system to be in a certain eigenstate

n
⟩

{\displaystyle \vert n \rangle}

 when the value of that operator measured is given by

⟨
n
Ψ
⟩

{\displaystyle \langle n \vert \Psi \rangle }

.

The way that the wavefunction changes over time is given by the Schrödinger equation. Various properties of the particle, such as position, momentum and energy, can be found by applying operators to the wavefunction.
Ray

A **ray** is a one-dimensional shape comprising half an infinite line, with a point as a boundary on one end. Because it is one dimensional with an uncountably infinite number of points and a single pointlike boundary, it is topologically equivalent to the half-open line segment.

It can be visualised as the nonnegative part of a number line covering all finite numbers, or alternately as the subset of the Euclidean line with nonnegative coordinates.
Rectified tesseractihemioctachoron

4 cuboctahedra

A **rectified tesseractihemioctachoron**is a uniform polychoron in the icositetrachoron regiment that can be constructed by rectifying a tesseractihemioctachoron.

Its Bowers acronym is **ratho**.

## Structure and Sections

The rectified tesseractihemichoron is in the same regiment as the icositetrachoron. This means that it has the same edge arrangement and edge count as an icositetrachoron. Being in the same regiment as the icositetrachoron also implies that the relationship between the circumradius and edge length of a rectified tesseractihemichoron is the same as icositetrachoron's, which is

1
l

{\displaystyle 1l}

 for edge length

l

{\displaystyle l}

.

The vertex figure of a rectified tesseractihemioctachoron is a **bowtie prism**.

### Subfacets

* 24 points (0D)
* 96 line segments (1D)
* 60 triangles (2D)
* 24 squares (2D)
* 8 octahedra (3D)
* 8 tetrahemihexahedra (3D)
* 4 cuboctahedra (3D)
* 1 **rectified tesseractihemioctachoron** (4D)

## See Also

**Have Full Hexadecachoric symmetry:** oh · shahoh · huhoh · hohoh · ohuhoh · ghahoh
**Have Full Demitesseractic symmetry:**
**ratho** · odho ·
hodho · hoh honho · dod honho · doh honho

## References

1. ↑ http://www.polytope.net/hedrondude/icoes.htm
2. ↑ https://bendwavy.org/klitzing/incmats/ratho.htm
Square tiling

The **square tiling** is a regular tiling formed of a plane filled with squares. It has a Schläfli symbol of

{
4
,
4
}

{\displaystyle \{4,4\}}

, as four squares join at each vertex. Its bowers acronym is **squat**.

## Colorings

There are nine different uniform colorings of the square tiling (in which the colors around each vertex are the same).

The following numbers label the colors around each vertex clockwise (for example "1212" shows that as you go clockwise around a vertex you find a square with color 1, then color 2, then color 1, then color 2 again, then it repeats).

The nine uniform colorings are:

* 1111 - this is the regular form.
* 1212 - this can be formed from the rectified square tiling, or

r
{
4
,
4
}

{\displaystyle r\{4,4\}}

.
* 1213 - this can be formed as the cantellated square tiling or

t

0
,
2

{
4
,
4
}

{\displaystyle t\_{0,2} \{4,4\}}

.
* 1122
* 1234
* 2 types of 1112
* 2 types of 1123

## Subfacets

* Infinite points (0D)
* Infinite line segments (1D)
* Infinite squares (2D)

## See Also

### Regular Hypercubic Tilings

* Apeirogon
* **Square tiling**
* Cubic honeycomb
* Tesseractic tetracomb
* Penteractic pentacomb

### Uniform Shapes with the Same Faces

{
4
,
2
}

{\displaystyle \{4,2\}}

{
4
,
3
}

{\displaystyle \{4,3\}}

{
4
,
4
}

{\displaystyle \{4,4\}}

{
4
,
5
}

{\displaystyle \{4,5\}}

{
4
,
6
}

{\displaystyle \{4,6\}}

{
4
,
7
}

{\displaystyle \{4,7\}}

{
4
,
8
}

{\displaystyle \{4,8\}}

{
4
,
∞
}

{\displaystyle \{4,\infty\}}

{
4
,

π
i

λ

}

{\displaystyle \{4, \frac{\pi i}{\lambda}\}}

### Uniform Shapes with the Same Faces per Vertex

{
2
,
4
}

{\displaystyle \{2,4\}}

{
3
,
4
}

{\displaystyle \{3, 4\}}

{
4
,
4
}

{\displaystyle \{4,4\}}

{
5
,
4
}

{\displaystyle \{5,4\}}

{
6
,
4
}

{\displaystyle \{6,4\}}

{
7
,
4
}

{\displaystyle \{7,4\}}

{
8
,
4
}

{\displaystyle \{8,4\}}

{
∞
,
4
}

{\displaystyle \{\infty,4\}}

{

π
i

λ

,
4
}

{\displaystyle \{\frac{\pi i}{\lambda},4\}}

### Uniform Tilings

t
0

{
4
,
4
}

{\displaystyle t\_0 \{4,4\}}

t
1

{
4
,
4
}

{\displaystyle t\_1 \{4,4\}}

t
2

{
4
,
4
}

{\displaystyle t\_2 \{4,4\}}

t

0
,
1

{
4
,
4
}

{\displaystyle t\_{0,1} \{4,4\}}

t

1
,
2

{
4
,
4
}

{\displaystyle t\_{1,2} \{4,4\}}

t

0
,
2

{
4
,
4
}

{\displaystyle t\_{0,2} \{4,4\}}

t

0
,
1
,
2

{
4
,
4
}

{\displaystyle t\_{0,1,2} \{4,4\}}
Rhombicosidodecahedron

12 pentagons

A (small) **rhombicosidodecahedron** is an Archimedean solid created from cantellating a dodecahedron or an icosahedron. Each edge of a pentagonal face of the dodecahedron is shared with a square and each vertex is shared with a triangle. Alternatively, the edges of a triangular face of an icosahedron are shared with squares and each vertex is shared with a pentagon.

A rhombicosidodecahedron has 12 pentagons, 30 squares, and 20 triangles.

Its Bowers acronym is **srid**.

## See Also

* Polytope Wiki. "Small rhombicuboctahedron".
* Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts".

t
0

{
5
,
3
}

{\displaystyle t\_0 \{5,3\}}

t
1

{
5
,
3
}

{\displaystyle t\_1 \{5,3\}}

t
2

{
5
,
3
}

{\displaystyle t\_2 \{5,3\}}

t

0
,
1

{
5
,
3
}

{\displaystyle t\_{0,1} \{5,3\}}

t

1
,
2

{
5
,
3
}

{\displaystyle t\_{1,2} \{5,3\}}

t

0
,
2

{
5
,
3
}

{\displaystyle t\_{0,2} \{5,3\}}

t

0
,
1
,
2

{
5
,
3
}

{\displaystyle t\_{0,1,2} \{5,3\}}

t

0
,
2

{
2
,
3
}

{\displaystyle t\_{0,2} \{2,3\}}

t

0
,
2

{
3
,
3
}

{\displaystyle t\_{0,2} \{3,3\}}

t

0
,
2

{
4
,
3
}

{\displaystyle t\_{0,2} \{4,3\}}

t

0
,
2

{
5
,
3
}

{\displaystyle t\_{0,2} \{5,3\}}

t

0
,
2

{
6
,
3
}

{\displaystyle t\_{0,2} \{6,3\}}

t

0
,
2

{
7
,
3
}

{\displaystyle t\_{0,2} \{7,3\}}

t

0
,
2

{
8
,
3
}

{\displaystyle t\_{0,2} \{8,3\}}

t

0
,
2

{
∞
,
3
}

{\displaystyle t\_{0,2} \{\infty,3\}}

t

0
,
2

{

π
i

λ

,
3
}

{\displaystyle t\_{0,2} \{\frac{\pi i}{\lambda},3\}}
Reality

The concept of reality is the state or quality of being real, essentially all of existence.

## In Terms Of Cosmology

A great example for reality as we understand would be Universe (ours), which is theorized to exist with 3 spatial dimensions, and 1 time dimension. One of the theories for a Multiverse is one in which we exist in a much bigger space with 9 spatial dimensions. Another is that our Universe exists in a hyper-massive black hole slowly pulling us towards the center, and that Multiple realities exist across the event horizon.

Realium is essentially just another name for Reality.

## Reality vs. Existence

While the term 'Existence' can serve as an synonym for Reality for some, there are in fact some key differences between the two concepts. "Reality" serves as a type of existence in which things are described as "real", while anything not real still exists in some form, but not in the same way as anything part of reality, or at least from the perspective of those within that reality. In short, Reality is what is considered real, and existence is things both real and unreal. Whatever somehow transcends this dichotomy, could transcend existence itself. Beyond is believed to hold such incomprehensible concepts.
Rhombitripseudogonal tiling

'"`UNIQ--postMath-00000003-QINU`"'

ℵ0 '"`UNIQ--postMath-00000002-QINU`"' pseudogons

A **rhombitripseudogonal tiling** is a uniform noncompact hyperbolic tiling constructed by cantellating an order-3 pseudogonal tiling.

Its faces consist of an infinite number of triangles, an infinite number of squares, and an infinite number of pseudogons of the same symmetry.

## Gallery

t

0
,
2

{
11
i
,
3
}

{\displaystyle t\_{0,2} \{11i, 3\}}

t

0
,
2

{
10
i
,
3
}

{\displaystyle t\_{0,2} \{10i, 3\}}

t

0
,
2

{
9
i
,
3
}

{\displaystyle t\_{0,2} \{9i, 3\}}

t

0
,
2

{
8
i
,
3
}

{\displaystyle t\_{0,2} \{8i, 3\}}

t

0
,
2

{
7
i
,
3
}

{\displaystyle t\_{0,2} \{7i, 3\}}

t

0
,
2

{
6
i
,
3
}

{\displaystyle t\_{0,2} \{6i, 3\}}

t

0
,
2

{
5
i
,
3
}

{\displaystyle t\_{0,2} \{5i, 3\}}

t

0
,
2

{
4
i
,
3
}

{\displaystyle t\_{0,2} \{4i, 3\}}

t

0
,
2

{
3
i
,
3
}

{\displaystyle t\_{0,2} \{3i, 3\}}

t

0
,
2

{
2
i
,
3
}

{\displaystyle t\_{0,2} \{2i, 3\}}

t

0
,
2

{
i
,
3
}

{\displaystyle t\_{0,2} \{i, 3\}}

## See Also

t

0
,
2

{
2
,
3
}

{\displaystyle t\_{0,2} \{2,3\}}

t

0
,
2

{
3
,
3
}

{\displaystyle t\_{0,2} \{3,3\}}

t

0
,
2

{
4
,
3
}

{\displaystyle t\_{0,2} \{4,3\}}

t

0
,
2

{
5
,
3
}

{\displaystyle t\_{0,2} \{5,3\}}

t

0
,
2

{
6
,
3
}

{\displaystyle t\_{0,2} \{6,3\}}

t

0
,
2

{
7
,
3
}

{\displaystyle t\_{0,2} \{7,3\}}

t

0
,
2

{
8
,
3
}

{\displaystyle t\_{0,2} \{8,3\}}

t

0
,
2

{
∞
,
3
}

{\displaystyle t\_{0,2} \{\infty,3\}}

t

0
,
2

{

π
i

λ

,
3
}

{\displaystyle t\_{0,2} \{\frac{\pi i}{\lambda},3\}}

t
0

{

π
i

λ

,
3
}

{\displaystyle t\_0 \{\frac{\pi i}{\lambda},3\}}

t
1

{

π
i

λ

,
3
}

{\displaystyle t\_1 \{\frac{\pi i}{\lambda},3\}}

t
2

{

π
i

λ

,
3
}

{\displaystyle t\_2 \{\frac{\pi i}{\lambda},3\}}

t

0
,
1

{

π
i

λ

,
3
}

{\displaystyle t\_{0,1} \{\frac{\pi i}{\lambda},3\}}

t

1
,
2

{

π
i

λ

,
3
}

{\displaystyle t\_{1,2} \{\frac{\pi i}{\lambda},3\}}

t

0
,
2

{

π
i

λ

,
3
}

{\displaystyle t\_{0,2} \{\frac{\pi i}{\lambda},3\}}

t

0
,
1
,
2

{

π
i

λ

,
3
}

{\displaystyle t\_{0,1,2} \{\frac{\pi i}{\lambda},3\}}