recursal/Fanatic-Fandom huggingface dataset:
Glider

A **glider** is a structure used by civilizations to travel between universes through interuniversal space. It takes the form of a wavepacket that is capable of travelling in the interuniversal medium by making use of disturbances in the field, created from within a universe.

Upon colliding with another universe, it creates a disturbance in the target. The shape of this disturbance can be incredibly complicated, and depends on the shape of the glider, which is determined when the glider is created but can also evolve as it travels. The very earliest gliders simply signal existing civilisations in the target universe; more sophisticated gliders can assemble nanofabricators out of dust and load them with a copy of the sender's values, as well as perform computations en-route.
Heptagonal prism

A **heptagonal prism** is a prism with a heptagon as the base. This makes in the cartesian product of a heptagon and a line segment.

It is also the truncated heptagonal hosohedron, which gives it heptagonal prismatic symmetry.

The Bowers acronym for a heptagonal prism is **hep**.

## Structure and Sections

The planar cross section of a heptagonal prism taken parallel to the base is a heptagon, identical to the base. The planar cross section taken perpendicular to the base is a rectangle, with the height of the rectangle equal to the height of the prism and the width dependant on where the cross section is taken.

## See Also

t

0
,
1

{
2
,
2
}

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

t

0
,
1

{
2
,
3
}

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

t

0
,
1

{
2
,
4
}

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

t

0
,
1

{
2
,
5
}

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

t

0
,
1

{
2
,
6
}

{\displaystyle {t}\_{0,1} \{2,6\}}

t

0
,
1

{
2
,
7
}

{\displaystyle {t}\_{0,1} \{2,7\}}

t

0
,
1

{
2
,
8
}

{\displaystyle {t}\_{0,1} \{2,8\}}

t

0
,
1

{
2
,
∞
}

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

t

0
,
1

{
2
,

π
i

λ

}

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

Template:Variant Nav t01 X 7
Template:Variant Nav 2 7
Echidnahedron

An **echidnahedron** is the seventeenth and outermost stellation of the icosahedron. When interpreted as a star polyhedron, it is composed of 20 self-intersecting irregular great enneagrammic faces.

It is named after an *echidna*, a small spiky egg-laying mammal due to the shape being very spiky in appearance.

## Structure and Sections

### Subfacets

* 60 points (0D)
* 90 line segments (1D)
* 20 great enneagrams (2D)
* 1 echidnahedron (3D)
Ericka walking down the grand staircase

Ericka: I like the jungle.

Leah Saliza: Where is Spy?

Ericka: Perhaps he is in a jungle holding a banana.

Rozalija: But I thought he is allergic to bananas. And we don't have jungles in this country.

Ericka: [facepalm] I was not talking about an actual banana. Or an actual jungle.

Leah Saliza: Are you dating now?

Ericka: Yes. We are going on a date in the jungle.

Leah Saliza: But we don't have jungles here.

Ericka: It's a faux jungle bar.

Rozalija: Why are you so obsessed with jungles?

Ericka: Because I am.

[later that day]

Ericka: So, what do you think of Funky Honeypop?

Phoebe: Meh. Whatever.

Ericka: [sees Spy] *And I feel like this love is supernatural*

*Oh oh*

*And if you want it I'll give it to you*

*Supernatural*

*Oh oh*

*And I feel like this love is supernatural*

*Oh oh*

*And if you want it I'll give it to you*

*Supernatural*

*Oh oh*

Spy: Oh. Hi.

Phoebe: Oh gravy baby baby baby baby baby baby baby baby baby baby baby

Ericka: I'm gonna lounge out here.

Leah Saliza: Spy is such a pervert!

Spy: Don't care.

Taylia: Hi, I am waiting for my KFC to arrive.

Emily: Taylia, I don't really care that you're waiting for your KFC to arrive.

Taylia: HOW DO YOU KNOW MY NAME?

Emily: Because you wrote it in Sharpie on your tits.

Taylia: I didn't write my name in Sharpie on my boobs!

Emily: Yes you did!

Spy: She didn't write her name in permanent marker on her breasts! But can she show them anyways?

Ericka: No, she did not write on her titties, Emily!

Emily: Geez man. I'm joking. Her dog's collar says "belongs to Taylia Forbes".

Yahtzee: Ugh, these peasants. [sips her wine] A peasant pool party?! Those peasants don't even have a pool at their own house!

Leah Saliza: Umm, I have a pool at my house. So yeah.
Heptadecagon

## Hypervolumes

### Surface Area

'"`UNIQ--postMath-00000004-QINU`"'

A **heptadecagon** is a 2-dimensional polygon with seventeen edges.

## Structure and Sections

### Hypervolumes

* vertex count =

17

{\displaystyle 17}
* edge length =

17
l

{\displaystyle 17l}
* surface area =

17
4

cot
⁡

(

π
17

)

l

2

{\displaystyle \frac{17}{4}\cot\left( \frac{\pi}{17} \right) {l}^{2}}

### Subfacets

* 17 points (0D)
* 17 line segments (1D)
* 1 heptadecagon (2D)

## See Also

Template:Variant Nav X2

t
0

{
15
}

{\displaystyle t\_0 \{15\}}

t
1

{
15
}

{\displaystyle t\_1 \{15\}}

t

0
,
1

{
15
}

{\displaystyle t\_{0,1} \{15\}}

## References

1. ↑ https://en.wikipedia.org/wiki/Heptadecagon
Euclid's Postulates

**Euclid's postulates** are a set of five postulates that describe Euclidean geometry.

1. There exists a line that contains two points
2. There exists a ray that contains two points
3. One can draw a circle by picking a center point, and a distance
4. All right angles (π∕2 radians) are congruent
5. Given a straight line and a point, there exists one parallel line that passes through the point

Some geometries, like hyperbolic geometry do not follow some, or all of these postulates.

Removing the parallel postulate (Axiom 5) gives a geometry called absolute geometry, of which hyperbolic geometry is an example. Removing the notions of distance and angle (Axioms 3 and 4) gives affine geometry. Removing distance, angle and parallel lines (Axioms 3, 4 and 5) gives ordered geometry.
Grand hecatonicosachoron

A **grand hecatonicosachoron** is a regular star polychoron with 120 dodecahedral cells. It is one out of ten Schläfli-Hess polytopes. Its dual is the great stellated hecatonicosachoron.

Its Bowers acronym is **gahi**.

## See Also

**Self-intersecting regular polychora:** fix · gohi · **gahi** · sishi · gaghi · gishi · gashi · gofix · gax · gogishi
**Tesseractihemioctachoron:** tho
Great stellated dodecahedron

The **great stellated dodecahedron** is a regular star polyhedron created from 12 pentagrammic faces, with three meeting at each vertex. It is one out of four stellations of the dodecahedron, with the other three being the dodecahedron, the great dodecahedron, and the small stellated dodecahedron.

Its Bowers acronym is **gissid**.

## See Also

**Self-intersecting regular polyhedra:** gad · sissid · gike · **gissid**
Euclidean realm

The **Euclidean realm** is a flat, infinitely large 3-dimensional space that follows the rules of Euclidean Geometry. It can be created by taking the cartesian product of three copies of the Euclidean line.

A realm can be used to bisect a teron, and polychora can have realms of symmetry through which they can be reflected. Taking multiple realmic cross sections of a polychoron can give insight into their structure; this is one method that can be used to visualise polychora without needing to picture a four-dimensional space.
Hendecealmverse

A **hendecealmverse** is a universe that occupies 11-Dimensional Space.

As usual, hendecealmverses 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.
Euclidean space

A **Euclidean space** is a zero-curve, infinitely large, real metric space that follows Euclidean geometry, and thus, all of Euclid's Postulates.

Euclidean spaces are constructed from repeated Cartesian products of a real line

R

1

{\displaystyle \mathbb R^{1}}

, and can be modelled with a **real coordinate space**

R

n

{\displaystyle \R^n}

 (often, Euclidean spaces are denoted with

R

n

{\displaystyle \R^n}

, though

E

n

{\displaystyle \mathbb{E}^n}

 can be used). This means that coordinates in a Euclidean space have to be an ordered tuple of real numbers, the number of numbers is the dimensionality of the space.

Euclidean spaces are typically known as "flat" spaces due to the fact that they have zero curvature.

Distances in a Euclidean space can be determined with the Pythagorean theorem.

Euclidean spaces can be generalised with Hilbert spaces, which can allow spaces to pertain an infinite dimensionality.

Spaces that don't follow Euclidean geometry do not follow one of the postulates, and may have curvature, imaginary dimensions, a different geometry.
Fantazia

Fantazia is the unique ruler of his own beyond-iteration, the reason being that there are no supergods or gods of any type, (including creator or destroyer) except himself.

## **Information**

What makes Fantazia so unique is that his entire beyond-iteration is his own dream, or more specifically, his own Imaginata, meaning that if he wanted, he could instantly change anything by force without any problems with a single thought, within his dream, making him effectively all-powerful within his version of beyond.

Outside of his dream, he is *obviously* not as powerful as he is within it, as entities equivalent to himself are still able to give him a challenge.

## **Appearance**

Fantazia's general appearance is meditating humanoid with a barrier around him floating through Transcendentem. When Fantazia turns into his entity form, this bubble vanishes and he is able to move throughout Transcendentem.
Inductor

An **inductor** is an ideal circuit element that has only inductance. Reluctance is also associated with this component; when the reciprocal quantity is used, it can also be called a **reluctor**.

When a changing current passes through an inductor, it creates a magnetic field (via Ampere's Law). This magnetic field then induces an electric field (via Faraday's law), creating a voltage drop that opposes the change in current.

## Inductance

An current I changing at a rate İ passing through an inductor L has a voltage drop V given by

# V
L

I
˙

{\displaystyle V = L\dot{I}}

.
Gongol

A **gongol** is a four-dimensional shape made from the solid interior of a glome. It is the four-dimensional hyperball.

## Structure and Sections

The gongol is composed of a single curved cell. Its sections look like a point growing into a ball before shrinking back.

### Hypervolumes

* vertex count =

0

{\displaystyle 0}
* edge length =

0

{\displaystyle 0}
* surface area =

0

{\displaystyle 0}
* surcell volume =

π

2

4

l
3

{\displaystyle \frac{{\pi}^{2}}{4} l^3}
* surteron bulk =

π

2

32

l
4

{\displaystyle \frac{{\pi}^{2}}{32} l^4}

### Subfacets

* 1 glome (3D)
* 1 gongol (4D)
Gidtuxthix

720 decagrams

5400 squares

1440 pentagons

2400 hexagons

720 decagons

120 small icosicosidodecahedra

120 rhombidodecadodecahedra

120 quasitruncated dodecadodecahedra

600 cubohemioctahedra

A **great ditrigonary hexacositetrishecatonicosahexacosichoron** is a uniform polychoron in the rectified great hecatonicosachoron regiment with 1200 vertices, 7200 edges, 16920 faces, and 1680 cells. It is an example of a polytope that is non-orientable and wild.

Its Bowers acronym is "**gidtuxthix**"

## Structure and Sections

The gidtuxthix is in the same regiment as the rectified small ditrigonary hexacosihecatonicosachoron (**rissidtixhi**). This means that it has the same edge arrangement and edge count as rissidtixhi. Being in the same regiment as rissidtixhi also implies that the relationship between the circumradius and edge length of a gidtuxthix is the same as rissidtixhi's, which is

l

3

{\displaystyle l{\sqrt {3}}}

 for edge length

l

{\displaystyle l}

.

The vertex figure of a gidtuxthix is variant of a faceted ditrigonal prism.

### Hypervolumes

* vertex count =

1200

{\displaystyle 1200}
* edge length =

7200
l

{\displaystyle 7200l}

### Subfacets

* 1200 points (0D)
* 7200 line segments (1D)
* 1440 pentagrams (2D)
* 4800 triangles (2D)
* 720 decagrams (2D)
* 5400 squares (2D)
* 1440 pentagons (2D)
* 2400 hexagons (2D)
* 720 decagons (2D)
* 600 octahedra (3D)
* 120 icosidodecahedra (3D)
* 120 small icosicosidodecahedra (3D)
* 120 rhombidodecadodecahedra (3D)
* 120 quasitruncated dodecadodecahedra (3D)
* 600 cubohemioctahedra (3D)
* 1 great ditrigonary hexacositetrishecatonicosahexacosichoron (4D)

## References

1. ↑ http://www.polytope.net/hedrondude/rissid.htm
2. ↑ https://bendwavy.org/klitzing/incmats/rissidtixhi.htm
Hendekasphere

A **hendekasphere** is a 11-dimensional surface produced by finding the set of all points that are an equal distance from another point in 12-dimensional space. Because it is curved, it is often represented embedded in 12-dimensional space. A dekasphere is the shape of the exterior of an dodekorb. It is the 11-dimensional hypersphere.
Giant star

A **giant star** is a type of very large, very bright star, generally seen towards the end of a stellar lifespan. Once a subgiant star's core finally collapses into a degenerate state and the star begins dredging heavy elements to its surface, it rapidly expands. Early-stage giants fuse hydrogen in their outer shells, much like subgiants, while higher-mass giants eventually begin fusing helium into carbon and oxygen by the triple-alpha process. On an H-R diagram, the giant branch is a large ellipse near the upper right (very bright but generally cool).

Solar-mass giant stars move from the giant branch to the "red clump" or horizontal branch, and from there to the much more luminous asymptotic giant branch. Higher-mass stars generally evolve directly to supergiants.

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

An **exotic polytope** is a polytope if it has more than two facets (n-1 dimensional subfacets) joined at at least one ridge (n-2 dimensional subfacets). This makes them distinct from true polytopes, which (if their dimensionality is greater than or equal to two) always have two facets joined together at their ridges. For instance, there are two edges joined together at a polygon's vertices, there are two faces joined together at a polyhedron's edges, there are two cells joined together at a polychoron's faces, and so on. The number of ridges an exotic polytope has can be considered ambiguous as ridges where multiple facets meet can be considered multiple coincident ridges. Examples of exotic polytopes include the three-dimensional great disnub dirhombidodecahedron (gidisdrid, Skilling’s figure) and small complex icosidodecahedron (cid) which have edges where multiple faces meet and the four-dimensional small exoditetrahedrary prismatotrishecatonicosachoron (seedatephi) which has pentagonal faces where multiple cells meet .

Polytopes that contain exotic polyhedra as elements, but do not have more than two facets joined at their ridges are called **exotic celled polytopes** (which can be generalized to any subfacet).

## References

1. ↑ http://www.polytope.net/hedrondude/glossary.htm#Exotic
2. ↑ https://bendwavy.org/klitzing/explain/compound.htm#exotic
Hexagonal tiling

The **hexagonal tiling** is a regular tiling formed from a plane filled with hexagons. Three hexagons join at each vertex. Its Bowers acronym is **hexat**.

## Structure and Sections

The hexagonal tiling can be represented in three different ways as a uniform tiling. It can be represented as {6,3} in regular form, t{3,6} as a truncated triangular tiling, or the omnitruncate of the 3-3-3 triangle group.

### Subfacets

* ℵ0 points (0D)
* ℵ0 line segments (1D)
* ℵ0 hexagons (2D)
* 1 hexagonal tiling (E2 tiling)

## See also

t
0

{
6
,
3
}

{\displaystyle t\_0 \{6,3\}}

t
1

{
6
,
3
}

{\displaystyle t\_1 \{6,3\}}

t
2

{
6
,
3
}

{\displaystyle t\_2 \{6,3\}}

t

0
,
1

{
6
,
3
}

{\displaystyle t\_{0,1} \{6,3\}}

t

1
,
2

{
6
,
3
}

{\displaystyle t\_{1,2} \{6,3\}}

t

0
,
2

{
6
,
3
}

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

t

0
,
1
,
2

{
6
,
3
}

{\displaystyle t\_{0,1,2} \{6,3\}}

t
0

{
(
3
,
3
,
3
,
)
}

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

t
1

{
(
3
,
3
,
3
,
)
}

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

t
2

{
(
3
,
3
,
3
,
)
}

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

t

0
,
1

{
(
3
,
3
,
3
,
)
}

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

t

1
,
2

{
(
3
,
3
,
3
,
)
}

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

t

0
,
2

{
(
3
,
3
,
3
,
)
}

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

t

0
,
1
,
2

{
(
3
,
3
,
3
,
)
}

{\displaystyle t\_{0,1,2} \{(3,3,3,)\}}
Inductance

**Inductance** is a physical quantity representing the ability of a change in current to induce an electromotive force. It has dimensions of [current]-2[mass][length]2[time]-2.

The idealised circuit element possessing only inductance is called an inductor. Inductance is related to the voltage and the time derivative of current by

# V
L

I
˙

{\displaystyle V = L\dot{I}}

.
Imaginary-order heptagonal tiling

An **imaginary-order heptagonal tiling**is a regular noncompact hyperbolic tiling with heptagonal faces and pseudogonal vertex figures.

## See Also

Template:Variant Nav 7 X

{
2
,

π
i

λ

}

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

{
3
,

π
i

λ

}

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

{
4
,

π
i

λ

}

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

{
5
,

π
i

λ

}

{\displaystyle \{5,\frac{\pi i}{\lambda}\}}

{
6
,

π
i

λ

}

{\displaystyle \{6,\frac{\pi i}{\lambda}\}}

{
7
,

π
i

λ

}

{\displaystyle \{7,\frac{\pi i}{\lambda}\}}

{
8
,

π
i

λ

}

{\displaystyle \{8,\frac{\pi i}{\lambda}\}}

{
∞
,

π
i

λ

}

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

{

π
i

λ
1

,

π
i

λ
2

}

{\displaystyle \{\frac{\pi i}{\lambda\_1},\frac{\pi i}{\lambda\_2}\}}
Euclidean line

A **Euclidean line** is a flat, infinitely large one-dimensional space following the laws of Euclidean geometry. It is often mistaken for a line segment, which is a connected subset of the line of finite length with two points as its boundary.

A line can be used to bisect a polygon; any linear cross section of a polygon will be a line segment. The way the length of this line segment changes can give information about the structure of the polygon. Polygons can also have lines of symmetry through which they can be reflected.

Because it has no endpoints, it is topologically equivalent to the open interval. It can be considered to be an open interval of infinite length.

A true line is an object with just length that exists at an abstract level only.

in comparison to something,imagine the shadow of a 2-Dimensional space, is non-existent to the 2-Dimensional space.
Inanimacy

**Inanimacy** is a category of sentience corresponding to a processing rate of zero bits per second. Inanimate beings, known as nonsentient, cannot store or process any information beyond what their physical composition allows - a rock chiseled with words, for example, is inanimate because it cannot make use of this information.

Inanimate beings are not "alive" in any agreed-upon sense, and are not generally counted as sentient to begin with.
Glominder

A **glominder** is a five-dimensional rotatope produced by the product of a line segment and a gongol; this means that it is a prism with a gongol as the base. It is composed of two gongols and a curved 4-D surface.

## Structure and Sections

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

The **heptacross** (also called **hectaicosaoctaexon**) is the 7-dimensional cross polytope. It is the dual of the hepteract. Its Bowers acronym is **zee**. Under the elemental naming scheme, it is called an **aeroexon**.

## Structure and Sections

The heptacross, as the 7-D cross polytope, can be considered a bipyramid of a hexacross.
Hypercube

A **hypercube** is a shape constructed by repeatedly taking the prism of a point (each prism being of identical length). Each hypercube has three hypercubes of the lower dimension surrounding each peak (e.g. a cube has three squares around each vertex, a tesseract has three cubes around each edge, etc.)
Exotic star

An **exotic star** is a hypothetical class of compact star that isn't necessarily composed of protons, neutrons, electrons or muons, but relatively stable under gravitational collapse through degeneracy pressure or some other method. Examples of exotic stars include quark stars, strange stars, electroweak stars, boson stars, preon stars, grey holes, and Planck stars. Most described exotic stars are denser than neutron stars, containing materials more dense than degenerate neutronium at their cores and are forms of exotic matter (in the broad sense); but are far less dense than black holes. The most well-understood of exotic stars are the quark stars, which are composed of free quarks in the form of quark-degenerate matter.
Icosagon

An **icosagon** is a 2-dimensional polygon with twenty edges.

## Structure and Sections

The regular icosagon has each angle at 162 degrees. It can be seen as a truncated decagon.

## See Also

t
0

{
10
}

{\displaystyle t\_0 \{10\}}

t
1

{
10
}

{\displaystyle t\_1 \{10\}}

t

0
,
1

{
10
}

{\displaystyle t\_{0,1} \{10\}}

t
0

{
20
}

{\displaystyle t\_0 \{20\}}

t
1

{
20
}

{\displaystyle t\_1 \{20\}}

t

0
,
1

{
20
}

{\displaystyle t\_{0,1} \{20\}}
Hyperverse

The **Hyperverse** is the 5D transfinite collection of all virtual shared space, created by the convergence of virtually enhanced physical reality and physically persistent virtual space, including the sum of all virtual worlds within lower dimensions (such as 4D and 3D), augmented reality, and cyberspaces such as the internet.

## **Misconception**

The Hyperverse has to do with real-life realities such as our universe which isn't the case; this term is used for the purpose of virtual reality/cyberspace which is based on gaming systems and online games that feature online play. It's only manipulated by Modders and or characters able to change the gaming/cyberspace. The Hyperverse is just a matrix of ones and zeros. The Hyperverse is similar to the metaverse in this way. This is where all of the records of our internet are kept.
Gǃkúnǁʼhòmdímà

Universe → Pisces–Cetus Supercluster Complex → Laniakea Supercluster → Virgo Supercluster → Local Group → Milky Way Galaxy → Orion-Cygnus Arm → Gould Belt → Local Bubble → Local Interstellar Cloud → Solar System → Scattered disc → **Gǃkúnǁʼhòmdímà**

## Physical Structure

### Density

1040 kg m-3 (based on effective diameter of 632 km)

### Diameter

632 km

**Gǃkúnǁʼhòmdímà**, provisional designation **2002 UK126**, is the currently the second-most massive named minor planet orbiting the Sun in the scattered disc behind Eris and a likely dwarf planet.

With an effective equivalent-sphere diameter between 600 and 670 km—comparable to very likely dwarf planets such as Ixion and Varuna and larger than planemos such as Enceladus, Miranda, Mimas, and the dwarf planet candidate Hygiea. However, measurements indicate that Gǃkúnǁʼhòmdímà is most likely not a spherical object. It is currently unknown whether or not Gǃkúnǁʼhòmdímà is currently in hydrostatic equilibrium.

Gǃkúnǁʼhòmdímàis in a binary systemwith a large moon named **Gǃòʼé ǃHú**. Gǃòʼé ǃHú is Gǃkúnǁʼhòmdímà’s only known moon and is roughly 142.8 km in diameter. Like Sedna and Gonggong, it is one of the reddest known trans-Neptunian objects.

## References

1. ↑ https://iopscience.iop.org/article/10.3847/0004-6256/152/6/156/pdf
2. ↑ https://www.sciencedirect.com/science/article/abs/pii/S0019103518306286?via%3Dihub
Enneagram

The **enneagram** is the two-dimensional star polygon with nine vertices, and every second vertex joined. The Bowers acronym for the enneagram is **eng**.

## Structure and Sections

### Hypervolumes

* vertex count =

9

{\displaystyle 9}
* edge length =

9
l

{\displaystyle 9 l}
* surface area =

9
4

cot
⁡

(

2
π

9

)

l
2

{\displaystyle \frac{9}{4} \cot \left( \frac{2\pi}{9} \right) l^2}

### Subfacets

* 9 points (0D)
* 9 line segments (1D)
* 1 enneagram (2D)

## See Also

t
0

{

9
2

}

{\displaystyle t\_0 \{\frac{9}{2} \}}

t
1

{

9
2

}

{\displaystyle t\_1 \{\frac{9}{2} \}}

t

0
,
1

{

9
2

}

{\displaystyle t\_{0,1} \{\frac{9}{2} \}}
Hypermatter

**Hypermatter** is a form of matter used in hypermatter drives for interuniversal communication. It is optimized for high density, to maximize the gravitational impression left behind in the other universe. Typically, it is built as a shrapnel of highly-charged rotating low-mass black holes, constantly maintained by an external stream of energy.

Due to only being gravitational in its operation, and weak at that, it is very low-fidelity; rather than using hypermatter directly, most civilisations quickly use the hypermatter's impression to construct a receiver in the target universe with which they can use the much more effective and compact infomatter.
Googological regions

**Googological regions** are huge spherical regions of our infinite universe proposed by Denis Maksudov as addition for his naming system of large numbers (i.e. of numbers generated using functions of fast-growing hierarchy and such ordinal notations as Cantor normal form, Veblen's function and Buchholz's function).

Googological regions defined as follows:

Ra

∙

{\displaystyle \bullet}

 is spherical region of the universe bounded by imaginary sphere with center at the Earth's center and with radius of

∙

{\displaystyle \bullet}

 meters, where

∙

{\displaystyle \bullet}

 is a name of number, which was created according this system of names (if name of number begins with a vowel, then don't write "a" in "Ra").

Example:
The Octinommwil is equal to

f

ψ
0

(

Ω

Ω

⋯

Ω

)

⏟

8

Ω
′

s

(
10
# )

f

ψ
0

(
Λ
[
9
]
)

(
10
)

{\displaystyle f\_{\underbrace{\psi\_0(\Omega\_{\Omega\_{\cdots\_{\Omega }}})}\_{8\quad\Omega's}}(10)=f\_{\psi\_0(\Lambda[9])}(10)}

 using fast-growing hierarchy and Buchholz's function. Then the Roctinommwil is spherical region of the universe bounded by imaginary sphere with center at the Earth's center and with radius of

f

ψ
0

(
Λ
[
9
]
)

(
10
)

{\displaystyle f\_{\psi\_0(\Lambda[9])}(10)}

 meters.

Bounders of those regions are not connected with existing real structures of the universe or with some inhomogeneities in the distribution of matter since we don't know anything about structures or inhomogeneities on so huge scales, but nevertheless any googological region can be defined at simple assumption that the space-time is infinite.

Note: instead light-years or parsecs for measure of astronomical distances the meter was chosen since it is base unit of the International System of Units (SI) but numbers mentioned above are so large that as a rule expressions don't change after convertion for light-years or gigaparsecs.

## Gallery

The galaxy Milky Way in the sky of planet of a binary star in a Globular cluster of the Large Magellanic Cloud. We can say that Milky Way and Large Magellanic Cloud as well as the whole observable universe belong, for example, to the Ratralum - googological region with radius of Tralum meters.

Picture was generated using Space Engine

## References

1. ↑ My system of number names (FGS) - Traveling To The Infinity
2. ↑ Space scale - Traveling To The Infinity
Hypergiant

A **hypergiant** is an extremely luminous, extremely massive supergiant star that is generally identified by its extremely high luminosity and very high mass loss rates. Hypergiants don't necessarily have to be larger than supergiants in radius, though, that is generally the case. Hypergiants are the stage that extremely massive O-type stars or Wolf-Rayet stars take on when their cores start collapsing.

When said star is about 15-20 times the mass of our sun, and has already passed the red supergiant or hypergiant stages, the star can go through an incredibly rare stage called a **yellow hypergiant** before moving to becoming a blue supergiant or hypergiant. Yellow hypergiants are scarcely populated, with only 15 known in our galaxy. This is likely due to the fact that stars of the mass required to achieve the stage are very rare and the stage doesn't last long.

When a hypergiant's core collapses, it can go out in an extremely powerful supernova, sometimes dubbed a **hypernova**, and the remnant is often a black hole.

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

**Entropy** is one of the thermodynamic state variables that describes the state of a thermodynamic system.

The change in entropy can be calculated based on the heat added to the system by

d
# S

δ

Q

r
e
v

T

{\displaystyle dS = \frac{\delta Q\_{rev}}{T}}

. It can also be defined in terms of microstates as

# S

k
B

ln
⁡
Ω

{\displaystyle S = k\_B \ln \Omega}

.

In any thermodynamic process, the total entropy of the system and its surroundings will either stay the same or increase - this is one statement of the second law of thermodynamics. This means that the entropy of the cosmos tends to a maximum, and there is a limit to the amount of thermodynamics that can be done.
Enneasphere

An **enneasphere** is a 9-dimensional surface produced by finding the set of all points that are an equal distance from another point in 10-dimensional space. Because it is curved, it is often represented embedded in 10-dimensional space. An enneasphere is the shape of the exterior of an dekorb. It is the 9-dimensional hypersphere.
Infinite rectangle

An **infinite rectangle** is a shape created from the Cartesian product of a line segment and a Euclidean line. It can be thought of as a rectangle with one of the pairs of parallel sides stretched infinitely in both directions or the space bounded between two infinite lines embedded in the Euclidean plane.
Fabulanaut

## Occupations

### Occupation:

Imaginarium ; Anywhere on the endless metafictional chain from first-order fiction to aleph-sub-fiction (also known as u(max)nreality)

## Powers and Abilities

### Powers:

Free traverse across story planes

**The Fabulanaut** [from latin *fabula* + suffix -*naut*] also refered to as the **Subtextual Diver** is a fictional character in such a story, wherein they are endowed with the ability to submerge into lower tiers of narrative existence.

They are bound to the world of fiction. Although their upper existential limit is the fourth wall (as they can never enter Reality), they do not have a lower limit: Fabulanaut of an n-tier field of existence – endowed with the ability of submersion into lower-order fields of existence by their author residing within (n+1)-tier field of existence – can submerge into as many subordinate stories as the narrator allows them to. Should the author so please, the Fabulanaut they conceive of could sink through the endless chain of subordinate stories, at the end of which resides Pauvre Chose, the powerless entity. This ability makes them a valuable asset to external parties mettling with nested realms of fiction and the boundaries dividing them. One such example are the Cosmic euthanisers, who sought out the services of the Fabulanaut in the past, hoping to find and eradicate Pauvre Chose under the conviction that to do away with misery in all its forms is an ethical imperative.

One might think of Fabulanaut as of a Demiurge, but only in their capacity not to be limited to a single cosmic entity tier. They are still a creation and full author authority is exercised over them. Likewise, they do not create their own stories, but rather intrude into those of others, offsetting their narrative intent, and corrupting their author authority, essentially overriding such authority with the authority of their creeator residing in a higher plane on the metafictional chain.

Fabulanaut serves as a counterexample to the claim that author authority over their fiction is absolute, as it proves that fictional author authority is not necessarily exercised by solely the author’s volition, but can in fact be intruded upon in spite of this volition. Fabulanaut can interact with the characters within a another person’s fiction without the will and sometimes even without the knowledge of this person, effectively entering others’ stories. Because of this ability to efectively enter works of art, the Fabulanaut is the most likely to reach the true meaning of an artwork through experiencing it from within. It is theorised that because of this probability of reaching true meaning, they are also likely to access the Domain of the Essence of Divine Art.
Heptagonal hosohedron

A **heptagonal hosohedron** is a 3-dimensional polyhedron with seven digonal faces. In normal Euclidean space, it is degenerate, but it can exist as a tiling of the sphere.

## See Also

{
2
,
0
}

{\displaystyle \{2,0\}}

{
2
,
1
}

{\displaystyle \{2,1\}}

{
2
,
2
}

{\displaystyle \{2,2\}}

{
2
,
3
}

{\displaystyle \{2,3\}}

{
2
,
4
}

{\displaystyle \{2,4\}}

{
2
,
5
}

{\displaystyle \{2,5\}}

{
2
,
6
}

{\displaystyle \{2,6\}}

{
2
,
7
}

{\displaystyle \{2,7\}}

{
2
,
8
}

{\displaystyle \{2,8\}}

{
2
,
∞
}

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

{
2
,

π
i

λ

}

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

t
0

{
7
,
2
}

{\displaystyle t\_0 \{7,2\}}

t
1

{
7
,
2
}

{\displaystyle t\_1 \{7,2\}}

t
2

{
7
,
2
}

{\displaystyle t\_2 \{7,2\}}

t

0
,
1

{
7
,
2
}

{\displaystyle t\_{0,1} \{7,2\}}

t

1
,
2

{
7
,
2
}

{\displaystyle t\_{1,2} \{7,2\}}

t

0
,
2

{
7
,
2
}

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

t

0
,
1
,
2

{
7
,
2
}

{\displaystyle t\_{0,1,2} \{7,2\}}

{
2
,
7
}

{\displaystyle \{2,7\}}

{
3
,
7
}

{\displaystyle \{3,7\}}

{
4
,
7
}

{\displaystyle \{4,7\}}

{
5
,
7
}

{\displaystyle \{5,7\}}

{
6
,
7
}

{\displaystyle \{6,7\}}

{
7
,
7
}

{\displaystyle \{7,7\}}

{
8
,
7
}

{\displaystyle \{8,7\}}

{
∞
,
7
}

{\displaystyle \{\infty,7\}}

{

π
i

λ

,
7
}

{\displaystyle \{\frac{\pi i}{\lambda}, 7\}}
E-Prime Chorus

The **E-Prime Chorus** is an infomatter-age multiversal civilisation that is localised around a single planet, E-Prime. Presently, it is made up of around ten billion alternate copies of E-Prime, in various states of development and integration with the Chorus, for a total population of around a quintillion.

It achieved this by being in a particularly dense region of the multiverse, with universes close enough that their gravitational influences on each other are non-negligable. Observations by several E-Primes of gravitational irregularities in space lead to them constructing a primitive receiver, possible with mere nanotechnology due to the proximity of the universes, and entering communications with each other.

The E-Prime Chorus maintains cohesion well due to its shared heritage: all versions of E-Prime have a similar culture and history, and indeed many of the founding E-Primes constructed their receivers with the eventual goal of unification into the Chorus.
Galaxy cluster

A **galaxy cluster** is a moderately large group of galaxies, generally no more than 1,000 total, which are associated either by gravitational attraction or because they simply formed alongside each other. Often, galaxy clusters will have very large elliptical galaxies or spiral galaxies at their center, around which the others orbit.

There are millions of galaxy clusters in our universe, and most of them are collectively bound into even larger structures called superclusters, filaments, or great walls.

As universes expand, it is likely that only the densest of galaxy clusters will stay together and eventually coalesce into enormous elliptical "supergalaxies" which will then slowly die out.
Heptealmverse

A **heptealmverse** is a universe that occupies 7-Dimensional Space.

As usual, hepteamverses 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.
Hyperbolic realm

The **hyperbolic realm** is an infinite 3-dimensional space that follows hyperbolic geometry, with a constant negative curvature throughout the entire space.

Spheres in the hyperbolic realm have the volume they enclose increase exponentially with radius, rather than polynomially like with spheres in the euclidean realm.
Horocycle

A **horocycle** is an curve infinite in length within a hyperbolic plane such that any two non-coincident lines that are perpendicular bisectors of the curve are limiting parallel lines. The centre of a horocycle is the ideal point that these lines asymptotically converge to. Any two horocycles are congruent. A horocycle is a one-dimensional horohypersphere.

A horcycle is the limit of circles or hypercycles that share a tangent line passing through a given point as their radii tend to infinity. Being a one-dimensional horohyperball, tilings of a one-dimensional Euclidean space (Euclidean line) embedded in a hyperbolic space will be circumscribed by a horocycle. The only uniform tiling of the Euclidean line is the apeirogon, which can be constructed by partitioning a Euclidean line into equal length line segments and defining one half-plane as the interior. Apeirogons in a hyperbolic plane can be constructed by partitioning a horocycle into equal length arcs, considering the union of all the line segments that connect the endpoints of each arc as the boundary, and the union of all the omega triangles defined by the ideal point and the endpoints of an arc as the interior.

In the Poincaré disk, horocycles are represented by circles internally tangent to the boundary circle. The point of tangency of the circle is the ideal point that is the centre of the horocycle.
Galaxy

A **galaxy** is a gravitationally bound collection of stars, interstellar gas and dust, nebulae, and usually some amount of dark matter. Galaxies take many different shapes; some of them are spherical or ellipsoidal (elliptical), some are flat and disc-like (lenticular) and may have spiraling arms of dense star-forming regions (spiral or barred spiral). Other times, they have no clearly defined shape (irregular) and resemble very large nebulae.

Galaxies range in size from just a few thousand to hundreds of thousands of lightyears across, and contain millions, billions, or trillions of stars. Our own galaxy, the Milky Way, is roughly 100,000 lightyears across and contains between 100 billion and 400 billion stars, a large fraction of which are in binary or triple systems.

A civilization that controls all of the resources available in an entire galaxy is called a Type 3.0 Civilization.

## Constituents

### Stars

The visible component of a galaxy is made up of stars, with galaxies containing a variable number of them, depending on the size of the galaxy. Dwarf galaxies contain a few billion stars (109), and giant galaxies can contain trillions of stars (1014).

### Stellar Remnants

Galaxies also contain stellar remnants, from stars that have died during the lifespan of the galaxy.

The most significant of these is a central black hole, present in many galaxies, with a mass that can be on the order of millions of times that of the Sun. Infalling matter leads to a vastly increased radiation production the center of the galaxy, creating something called an active galactic nucleus.

### Interstellar Gas

Interstellar gas is the sparse gas that is between stars, with varying density. The densest interstellar gas is cold phase (~102 K), found in molecular clouds, where new stars are formed in the spiral arms. There is also the warm phase (~104 K), found between molecular clouds, and the hot phase (~106 K), resulting from gas that has been shock heated by recent supernovae.

### Cosmic Dust

Cosmic dust is made up of small solid grains that are found in the interstellar medium and released from supernovas as they fuse dense elements.

### Dark Matter

The most major component of the galactic mass is dark matter, making up the majority of the mass of a galaxy. Dark matter exists in a diffuse halo around the galaxy, and does not interact with any of the fundamental forces other than gravity. This leads to an unusual rotation curve for the galaxy, with velocity being roughly constant with distance rather than falling off as would be expected.
Face

The **faces** of a polytope are two dimensional elements of a polytope that bound polyhedra. Faces of a polytope can be created when two or more cells meet each other. A polygon has a single face.

The term "n-face" is sometimes used to refer to an "n-subfacet" of a polytope, for example, tera of a 5-dimensional polyteron can be called its 4-faces.

2-dimensional faces are the facets of a polyhedron, the ridges of a polychoron, and the peaks of a polyteron.

The total area of a polytope's faces is called its surface area, or just area, if it's of a polygon.

## See Also

...Spire · Peak · Ridge · Facet · Polytope
Ganymede

Universe → Pisces–Cetus Supercluster Complex → Laniakea Supercluster → Virgo Supercluster → Local Group → Milky Way Galaxy → Orion-Cygnus Arm → Gould Belt → Local Bubble → Local Interstellar Cloud → Solar System → Jovian System → **Ganymede**

**Ganymede** is the third moon of the gas giant Jupiter. It is Jupiter's largest moon as well as the largest moon in the solar system, being twice the mass of Earth's moon and even 8% larger than the planet Mercury, even though it only has half the mass of the Solar System's smallest planet. This is due to Ganymede being mostly comprised of water and silicates. It is also suspected that not all of the water on Ganymede is frozen and that the planet could have subsurface oceans. This has led some people to believe, that life might be possible within those oceans, although most likely only primitive bacteria-like lifeforms.

Ganymede's name comes from Greek mythology, where he was a beautiful mortal man, who was abducted by the gods to serve as Jupiters/Zeus' cup-bearer.
Great heptagram

The **great heptagram** is a 2-Dimensional star polygon with seven sides, and every third vertex joined. The Bowers acronym for a great heptagram is gahg.

Each internal angle of a great heptagram is equal to 180/7 degrees, or approximately 25.7.

## Structure and Sections

#### Subfacets

* 7 points (0D)
* 7 line segments (1D)
* 1 great heptagram (2D)

## See Also

t
0

{

7
3

}

{\displaystyle t\_0 \{\frac{7}{3} \}}

t
1

{

7
3

}

{\displaystyle t\_1 \{\frac{7}{3} \}}

t

0
,
1

{

7
3

}

{\displaystyle t\_{0,1} \{\frac{7}{3} \}}
Hexealmverse

A **hexealmverse** is a universe that occupies 6-Dimensional Space.

As usual, hexealmverses 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.
Great icosahedron

A **great icosahedron** is a three-dimensional regular polyhedron with 20 faces, each of which is triangular. Around each vertex, faces are arranged in a pentagrammic formation. It has a Bowers' acronym of **gike**.

## See Also

**Self-intersecting regular polyhedra:** gad · sissid · **gike** · gissid

Template:Variant Nav 3 frac 5 2
Template:Variant Nav X frac 5 2
Icosidodecahedron

An **icosidodecahedron** is a uniform polyhedron and an Archimedean solid created from rectifying a dodecahedron or icosahedron. It has 12 pentagonal faces and 20 triangular faces. Each edge of a pentagonal face is shared with a triangle, and every vertex is shared by two pentagons and two triangles.

It's Bowers acronym is **id**.

## Symbols

Dynkin symbols of the icosidodecahedron include:

* o5x3o (uniform)
* xoxfo5ofxox&#xt (pentagonal gyrobirotunda)
* oxFfofx3xfofFxo&#xt (triangular symmetry)
* VooFxf oVofFx ooVxfF&#zx (block symmetry)

## Hypervolumes

* Vertex count =

30

{\displaystyle 30}
* Edge length =

60
l

{\displaystyle 60l}
* Surface area =

(
5

3

3

25
10

5

)

l
2

{\displaystyle (5\sqrt{3}+3\sqrt{25+10\sqrt{5}})l^2}
* surcell volume =

(
45
17

5

)

l
3

{\displaystyle (45+17\sqrt{5})l^3}

## Subfacets

* 30 points (0D)
* 60 line segments (1D)
* 12 pentagons (2D)
* 20 triangle (2D)
* 1 icosidodecahedron (3)

## Radii

* Vertex radius:

1

5

2

l

{\displaystyle \frac{1+\sqrt{5}}{2}l}
* Edge radius:

5
2

5

2

l

{\displaystyle \frac{\sqrt{5+2\sqrt{5}}}{2}l}
* Pentagon radius:

5
2

5

5

l

{\displaystyle \frac{\sqrt{5+2\sqrt{5}}{5}}l}
* Triangle radius:

(
3

3

15

)
l

{\displaystyle (3\sqrt{3}+\sqrt{15})l}

## Angles

* Dihedral angle:

arccos
⁡
(

5
2

5

15

)

{\displaystyle \arccos( \sqrt{\frac{5+2\sqrt{5}}{15}})}

​

## Vertex coordinates

The coordinates of the icosidodecahedron are:

* (±2φ,0,0) and all permutations
* (±φ^2,±φ,±1) and all even permutations

These coordinates show that a regular octahedron can be inscribed into the vertices of an icosidodecahedron.

## Related shapes

* Dual: Rhombic triacontahedron
* Vertex figure: Rectangle, sides 1 and φ
* Conjugate: Great icosidodecahedron
* Caps: Pentagonal rotunda
* Gyrations: Pentagonal orthobirotunda
* Regiment members: 3 (other uniform members: small icosihemidodecahedron, small dodecahemidodecahedron)

## See Also

* Polytope Wiki. "Icosidodecahedron"

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
1

{
2
,
3
}

{\displaystyle t\_1 \{2,3\}}

t
1

{
3
,
3
}

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

t
1

{
4
,
3
}

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

t
1

{
5
,
3
}

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

t
1

{
6
,
3
}

{\displaystyle t\_1 \{6,3\}}

t
1

{
7
,
3
}

{\displaystyle t\_1 \{7,3\}}

t
1

{
8
,
3
}

{\displaystyle t\_1 \{8,3\}}

t
1

{
∞
,
3
}

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

t
1

{

i
π

λ

,
3
}

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

t
1

{
2
,
5
}

{\displaystyle t\_1 \{2,5\}}

t
1

{
3
,
5
}

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

t
1

{
4
,
5
}

{\displaystyle t\_1 \{4,5\}}

t
1

{
5
,
5
}

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

t
1

{
6
,
5
}

{\displaystyle t\_1 \{6,5\}}

t
1

{

ℵ
0

,
5
}

{\displaystyle t\_1 \{\aleph\_0,5\}}
Great stellated hecatonicosachoron

A **great stellated hecatonicosachoron** is a regular star polychoron composed of 120 great stellated dodecahedral cells. It is one out of ten Schläfli-Hess polytopes and its dual is the grand hecatonicosachoron.

Its Bowers acronym is **gishi**.

## See Also

**Self-intersecting regular polychora:** fix · gohi · gahi · sishi · gaghi · **gishi** · gashi · gofix · gax · gogishi
**Tesseractihemioctachoron:** tho
Forcicium

**Forcicium** is a material made of condensed forces, like electromagnetism, which is incredibly versatile, being able to be molded into almost anything.

Due to the fact it is made entirely out of forces, destroying forcicium is impossible without advanced technology. Forcicium can also be used to create gates, that can be activated or deactivated to let objects in and out. However, forcicium is incredibly dangerous when not controlled. Due to being condensed force, it can return to being a normal force, releasing incredible amounts of energy, which can be weaponized, but in most cases is a danger that must be avoided. Forcicium is volatile when not controlled. If it is made of electromagnetism, it would have strange electromagnetic effects, making its containment difficult, if the system controlling it is electron-based technology.

Forcicium is usually harvested from protoverses due to the unity of physics, and intense forces there.
Great grand stellated hecatonicosachoron

A **great grand stellated hecatonicosachoron** is a regular star polychoron with 120 great stellated dodecahedral cells. It is a Schläfli-Hess polytope and is the only one with 600 vertices. The great grand stellated hecatonicosachoron is the stellated hecatonicosachoron and its dual is the grand hexacosichoron.

Its Bowers acronym is **gogishi**.

## See Also

**Self-intersecting regular polychora:** fix · gohi · gahi · sishi · gaghi · gishi · gashi · gofix · gax · **gogishi**
**Tesseractihemioctachoron:** tho