recursal/Fanatic-Fandom huggingface dataset:
Horizon breaking

**Horizon breaking** is a technology that some cosmic civilisations develop in universes with compatible laws of physics that allows them to travel beyond event horizons. After the development of this technology, events beyond the horizon can influence events that are not beyond the horizon, so the horizon ceases to be meaningful - it is 'broken'.

Horizon breaking can be separated into two types, called local and global horizon breaking.

Local horizon breaking entails producing single artifacts that can pass through event horizons, such as spacecraft equipped with warp drives or tachyon communicators. To advanced civilisations, this is often not considered to be true horizon breaking; if the laws of physics already support FTL, then horizon breaking could occur naturally so there never was an event horizon.

Global horizon breaking entails changing the laws of physics of the entire universe such that the event horizon can no longer exist, such as by causing something analogous to a false vacuum collapse that alters the geometry of spacetime to allow for events to propagate faster. This is often dangerous for beings inside the universe, and requires vast amounts of mass-energy, so true horizon breaking is typically only performed by multiversal civilizations.
Great wall

A **great wall** is a supermassive hypergalactic structure constructed of walls of galaxies, a galaxy filament. A galaxy filament is a massive wall of galaxies and a Great Wall is usually a particularly large galaxy filament. Great walls are the largest known structures in the universe, the most famous example of a Great Wall is the Sloan Great Wall, which is 1.38 billion light years long, the second largest Great Wall in our universe after Hercules–Corona Borealis Great Wall, which is 10 billion light years long.
Euclidean plane

*This article is about the geometrical figure. Not to be confused with Plane.*

The **Euclidean plane** is a flat, infinitely large two-dimensional space following the rules of two-dimensional Euclidean geometry. It can be formed from the Cartesian product of two copies of the Euclidean line.

A plane can be used to bisect a cell, and cells can have planes of symmetry through which they are reflected. The place at which a cell intersects a plane gives a two-dimensional shape and the change in shape as the cell passes through the plane can give information about the structure of the cell.

There is more than one way to make a 2D Cartesian plane. You could say the lines should be slightly slanted, as long as they parallel.
Galaxy group

A **galaxy group** is a smaller grouping than a galaxy cluster, usually consisting of 50 or fewer large galaxies and the several hundred various dwarf galaxies orbiting them. Some of them are very compact, with galaxies so close that they interact with each other regularly.

They can be grouped together into galaxy clusters or superclusters. There are likely millions or billions of galaxy groups in our universe alone.

Our own local group is a very small galaxy group consisting of the Milky Way, the Andromeda Galaxy, and the Triangulum Galaxy, along with their dozens of dwarf galaxies.
Dwarf spherical galaxy

**Dwarf spherical galaxies** (also referred to as **dwarf spheroidal galaxies)** are among the smallest and most common type of galaxy. They are extremely small and faint, and only a few have been discovered in Earth's Local Group, but it is likely that most galaxies have several spheroidal companions. Many dwarf spheroidal galaxies resemble globular clusters, and distinguishing the two can be difficult.

Most of the Milky Way's and Andromeda (M31)'s companion galaxies are of this type.
Hypercomplexverse

**Hypercomplexverses** are a type of verse such that all positions form tuples ("vectors") of some variety of hypercomplex number, a generalization of complex numbers. A hypercomplex number system is a term used to refer to a unital not necessarily associative algebra over the field of real numbers. These hypercomplex number systems include, but are not limited to, the Cayley-Dickson algebras, the composition algebras over the field of real numbers or the field of complex numbers, multicomplex numbers, and Clifford algebras. The only hypercomplex number systems that form a field are the real numbers and the complex numbers.

Generally, either the cardinality of the tuple or the cardinality of the tuple multiplied by the real-dimensionality of the algebra are considered to be dimensionality of the -verse's space. The latter is nicer if one want to consider it a space of real numbers. This space with addition and scalar multiplication is a vector space iff the hypercomplex number system forms a field and a module iff the hypercomplex number system forms a ring. This means that the only hypercomplex numbers whose space is vector space are verses whose positions are vectors of real numbers (meaning that the space is Euclidean. Flat universes satisfy this condition) and ones whose positions are vectors of complex numbers. The latter is typically known as a complexverse.

Hypercomplexverses may also pertain hypercomplex time and the spacetime itself analogous to real spacetimes, the behaviour of the spacetime may also restrict properties such as mass and hold curious properties such as length contraction and time dilation if causality is to be preserved. Objects that have complex mass are considered to be forms of exotic matter and the definition can be relaxed to incorporate objects that have, in a sense, hypercomplex mass. The "distance function" induced by the space(time)'s bilinear form (if the numbers with arithmetic at least form a ring) may still be useful as as a function whose range is the non-negative real numbers, however many properties that said function pertains in a Euclidean space or complex vector space may not be preserved. Hypercomplex analogues of Newtonian and Minkowski spacetime (such as

C

0
,
1

{\displaystyle {\mathbb {C}}^{0, 1}}

 or

C

3
,
1

{\displaystyle {\mathbb {C}}^{3, 1}}

) can be pertained by hypercomplexverses.

Another way of thinking about hypercomplexverses is that they are just -verses where positions in spacetime are tuples of real numbers and that the -verse just has a very exotic spacetime.

The following hypercomplexverses have pages on this wiki:

* Complexverse
* Quaterniverse
* Octoniverse
Extraterrestrial Life

Extraterrestrial Life is other lifeforms outside of Earth.

## In our Solar System

Earth is the only planet (so far) known to inhabit life. Humans like us would be unable to survive on the known planets in our solar system. But perhaps certain other life forms would be able to survive in the harsh conditions of other worlds.

## Research

Extraterrestrial life can be roughly grouped into two categories. The first is the broad classification of life itself, a process that includes microbial and other simple forms.

Without civilization and technology, life cannot produce the advanced signals that travel across the galaxy. However, many scientists continue to investigate atmospheres and other characteristics of worlds both in and out of the solar system as part of the search for life beyond our planet.

## What we've said

What we at this wiki have said (on other pages) is not meant to be taken as fact. Pages like The Folded Cascade are meant as fiction.
False matter

**False matter** is a type of matter with the property that things that are made of false matter are not made of false matter. It can safely be manipulated with few restrictions by omnipotent^2 entities and above, such as the Supergod Council; lower omnipotents, such as the Destroyer, can manipulate it with the aid of equipment produced by omnipotent^2 entities. False matter has some overlap with the trosinic element Bet, which under ordinary conditions behaves as false matter and is the primary form of false matter in the Transcendent neighbourhood of the local Beyond bubble.

## Uses

Shaped false matter charges serve as a useful weapon to annihilate misbehaving archverse chains - two subcritical hemiomnispheres of false matter can be combined in order to create a contradiction that explodes and fragments the chain into smaller components that can be eaten by micrological entities.
Dyck's surface

**Dyck's surface** is a two-dimensional non-orientable surface with an Euler characteristic of -1. It can be formed from the connected sum of three real projective planes, or as the connected sum of a torus and a real projective plane.

## Structure and Sections

As the non-orientable closed surface with an Euler characteristic of -1, it is homeomorphic to all other non-orientable closed surfaces with three crosscaps due to the classification theorem of closed surfaces.

## See Also

S

2

{\displaystyle \mathbb S^{2}}

R
P

2

{\displaystyle \mathbb{RP}^2}

2

R
P

2

{\displaystyle 2\mathbb{RP}^2}

3

R
P

2

{\displaystyle 3\mathbb{RP}^2}
Guardians of Aleph

The **Guardians of Aleph** are a group of cosmic beings that are supposedly, according to their mission statement, responsible for "protecting the Verse Cores against external threat". However, in doing so, they ruthlessly exterminate every civilization and entity that seems to be anything close to dangerous. They have several enemies, such as the Odhinites, and the Apeirocoalition.

Their organization spans uncountably many archverses and similarly high-level structures, and encompasses untold infinities of Kardashev Type-Infinity civilizations assisting them with their research and mission.
Hypersociality

**Hypersociality** is a category of sentience corresponding to a processing rate of 1032 bits/sec (a sentience quotient of 30-40 for a 100 kg individual).

Hypersocial sentient individuals are able to innately understand not only the workings of their own society, but also the interrelationships between multiple societies. This allows them to easily form fully integrated Type 3.0 Civilizations from communication between multiple stellar cultures.

## References

* http://www.xenology.info/Xeno/25.2.2.htm
Infinite-dimensional space

An **infinite-dimensional space** is a space with an infinite amount of dimensions, which means that a point's location would have to be defined using a Infinite amount of numbers,examples of this are Hilbert space or Banach space.

A verse with countably infinite dimensions is called a Omegealmverse.
Hygiea

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 → Asteroid belt → **Hygiea**

## Climate

### Temperature

-109.15 °C

**Hygiea** is the fourth-largest and fourth most massive asteroid and likely dwarf planet in the Asteroid belt and is the largest carbonaceous asteroid in the asteroid belt, comparable in size to Pallas. Because of its surface is comprised of carbonaceous materials, it is very dark in colour and is very dim. Combined with its large semi-major axis compared with other asteroids, it is why six much smaller asteroids were discovered before it on Earth.

In shape, Hygiea is an oblate spheroid that is very close to spherical in shape which is at least consistent with that of bodies in hydrostatic equilibrium. If Hygiea was in hydrostatic equilibrium, it will qualify as a dwarf planet and the second-largest and second-smallest known dwarf planet orbiting in the Asteroid belt. However, Hygiea's shape is not due to hydrostatic equilibrium, but a head-on collision that disrupted its formation in a manner that allowed it to become nearly spherical.

## References

1. ↑ https://www.eso.org/public/archives/releases/sciencepapers/eso1918/eso1918a.pdf
2. ↑ https://arxiv.org/abs/2007.08059
Great rhombicosidodecahedron

12 decagons

The **great rhombicosidodecahedron** is a uniform polyhedron and an Archimedean solid created by truncating an icosidodecahedron. It has 30 square faces, 20 hexagonal faces, and 12 decagonal faces.

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

## See Also

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\}}
Grand stellated hecatonicosachoron

A **grand stellated hecatonicosachoron** is a regular star polychoron with 120 small stellated dodecahedral cells. It is one of ten Schläfli-Hess polytopes, and one of two of them that are self-dual (the other being the great hecatonicosachoron).

Its Bowers acronym is **gashi**.

## See Also

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

The **Hamiltonian operator**,

H
^

{\displaystyle \hat{H}}

, is an operator in quantum mechanics that gives the sum of the kinetic and potential energy of a system; it is also the sum of the kinetic energy operator and the potential energy operator.

Because it gives the total energy of the system, it is also equal to the energy operator when acting on a wavefunction; this equality is written as

H
^

∣
ψ
# ⟩

E
^

∣
ψ
⟩

{\displaystyle \hat H \mid \psi \rangle = \hat E \mid \psi \rangle}

, and is known as the time-dependent Schrödinger equation.

## Representation

In the position representation, the Hamiltonian operator for a single, non-relativistic particle of mass m in a position-dependent potential V is

H
^

=
−

ℏ
2

2
m

∇
2

V

{\displaystyle \hat H = - \frac{\hbar^2}{2m} \nabla^2+V}

.
Gogoract

## Hypervolumes

### Vertex Count

'"`UNIQ--postMath-00000001-QINU`"'

A **gogoract** is a 10100-D hypercube, a hypercube with a googol dimensions.

## Structure and Sections

A gogoract with an edge length

l

{\displaystyle l}

 of has a largest diagonal of

10

50

l

{\displaystyle 10^{50}l}

. The googol-dimensional hypervolume of a gogoract is

l

10

100

{\displaystyle l^{10^{100}}}

.
Hypersphere

For (n + 1)-dimensional Euclidean space

R

n
1

{\displaystyle \R^{n+1}}

 the hypersphere (n-sphere)

S
n

{\displaystyle S^n}

 of radius *r* and center *c* is the set of all points that are at the same distance *r* from point *c*:

S
n

=

{

x
∈

R

n
1

d
(
x
,
c
# )
r

}

{\displaystyle S^n = \left\{ x \in \mathbb{R}^{n+1} | d(x,c) = r \right\} }

where

d
(
x
,
c
)

{\displaystyle d(x,c)}

 is euclidean metric for (n+1)-dimensional space

d
(
x
,
c

# i
1

n
1

(

x
i

−

c
i

)
2

{\displaystyle d(x,c)=\sqrt{\sum\_{i=1}^{n+1} (x\_i - c\_i)^2}}

Examples:

* For 2-dimensional Euclidean space the hypersphere is circle (1-sphere),
* For 3-dimensional Euclidean space the hypersphere is sphere (2-sphere).
* For 4-dimensional Euclidean space the hypersphere is glome (3-sphere).
Gould Belt

Universe → Pisces–Cetus Supercluster Complex → Laniakea Supercluster → Virgo Supercluster → Local Group → Milky Way Galaxy → Orion-Cygnus Arm → **Gould Belt**

The **Gould Belt** is a stellar belt around around 3,000 light years across, containing many O- and B-type stars, around 30 to 50 million years old, potentially formed by a collision between a gas cloud and a dark matter clump.

## References

1. ↑ Bekki, K.; Dark impact and galactic star formation: origin of the Gould belt
Great hecatonicosachoron

A **great hecatonicosachoron** is a regular star polychoron with 120 great dodecahedral cells. It is one out of ten Schläfli-Hess polytopes and one of two of them that are self-dual, the other being the grand stellated hecatonicosachoron.

Its Bowers acronym is **gohi**.

## See Also

**Self-intersecting regular polychora:** fix · **gohi** · gahi · sishi · gaghi · gishi · gashi · gofix · gax · gogishi
**Tesseractihemioctachoron:** tho
Expedition Ω-1A

**Expedition Ω-1A** was the final expedition sent out by The Cosmic Reconnaissance before the division ceased operation, due to the disappearance of all of the expedition's members.

## **Information**

This expedition was the most successful out of all of them, seeing as the Omnius-Infinity perfected Dimension Propulsion, which was a propulsion device that could leap extremely large distances by pulling itself into and out of certain dimensions. Doing so would allow the expedition to jump across the Archverse chain within a few months and exit the Omniverse.

Ultimately, the expedition failed due to the crew's evil intentions to exit the Omniverse and gain power, like deities being discovered by The Supergod Council, and 9/10 of its members being erased, while Satoru was sent to the Kalyubi Dimension and became Kotoblade.
Hyperbolic space

**Hyperbolic space** is space that exhibits a constant negative curvature. Although it is diffeomorphic and topologically equivalent to a Euclidean space, it pertains hyperbolic geometry, which gives it very different geometrical properties (such as high order tilings).

A universe with hyperbolic geometry is known as an open universe, in contrast to a closed universe with elliptic geometry.
Eccentricity

**Eccentricity**, simply put, is the measure of how much a conic section deviates from a perfect circle.

* The eccentricity of a circle is 0.
* The eccentricity of an ellipse is a real number between 0 and 1 given by the formula.
* The eccentricity of a parabola is always 1.
* And the eccentricity of a hyperbola is a real number greater than 1 given by the forumla.

The term "**first eccentricity**" is sometimes used for eccentricity to distinguish it from **second eccentricity** and **third eccentricity**, which is defined for both ellipses. Below is a chart that shows how to calculate the first, second and third eccentricities of conics, along with **linear eccentricity** (defined for ellipses and hyperbolae). Linear eccentricity is defined as the distance between the center and a focal point of an ellipse or hyperbola.

## Orbital eccentricity

Eccentricity is important to astrodynamics in the form of **orbital eccentricity**, which is the measure of how much an orbit or trajectory deviates from a perfect circle. Circular orbits have an eccentricity of 0, elliptic orbits have an eccentricity between 0 and 1, parabolic trajectories have an eccentricity of 1, and hyperbolic trajectories have an eccentricity greater than 1.

The eccentricity can be given with the formula

1
−

2
E

L
2

m

r
e
d

α
2

{\displaystyle \sqrt{1-\frac{2EL^2}{m\_{\rm red}\alpha^2}}}

where

E

{\displaystyle E}

 is the total orbital energy,

L

{\displaystyle L}

 is the angular momentum,

m

r
e
d

{\displaystyle m\_{\rm red}}

 is the reduced mass and

α

{\displaystyle \alpha}

 is the coefficient of the inverse-square law central force. Below is a table of the eccentricities of well-known objects.
Grand Unified Universe

### Contents

Elementary particles probably not uniting to make up any form of cohesive matter.

## Size

### Dimensionality

3+1

The **Grand Unified Universe** is an extremely unstable universe that has not achieved total division of the fundamental forces where it seemed that the Grand Unification Epoch of said universe has frozen in time. Here is where normal matter, i.e ours, is impossible but new forms of physics and laws can apply here. The Grand Unified Universe is also extremely hot but not as hot as string temperature.
Hexorb

A **hexorb** is the 6-dimensional solid interior of a pentasphere. It is the 6-dimensional hyperball.

## Structure and Sections

### Hypervolumes

* vertex count =

0

{\displaystyle 0}
* edge length =

0

{\displaystyle 0}
* surface area =

0

{\displaystyle 0}
* surcell volume =

0

{\displaystyle 0}
* surteron bulk =

0

{\displaystyle 0}
* surpeton pentavolume =

π

3

32

l

5

{\displaystyle \frac { { \pi }^{ 3 } }{ 32 } { l }^{ 5 }}
* surecton hexavolume =

π

3

384

l

6

{\displaystyle \frac { { \pi }^{ 3 } }{ 384 } l^{ 6 }}

### Subfacets

* 1 pentasphere (5D)
* 1 hexorb (6D)
Grand hexacosichoron

A **grand hexacosichoron** is a regular star polychoron with 600 tetrahedral cells. It is one of ten regular Schläfli-Hess polytopes and is the only one composed of 600 cells. The grand hexacosichoron is a stellated hexacosichoron and its dual is the great grand stellated hecatonicosachoron.

Its Bowers acronym is **gax**.

## See Also

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

A **hexagon** is a 2-dimensional polygon with six edges. The Bowers acronym for a hexagon is **hig**. It is one of the regular polygons that can tile 2-D space forming the hexagonal tiling, unlike pentagons, which cannot tile the plane. Hexagons have the greatest numbers of edges and angles of any regular polygon that can tile the plane.

## Symbols

Dynkin symbols for the hexagon include:

* x6o (regular)
* x3x (ditrigon)
* ho3oh&#zx (triambus)
* xu ho&#zx (rectangle symmetry)
* xux&#xt
* ohho&#xt

## Structure and Sections

The regular hexagon has equal edge lengths and each angle as 120 degrees. It can be seen as a truncated triangle.

### Hypervolumes

* vertex count =

6

{\displaystyle 6}
* edge length =

6
l

{\displaystyle 6l}
* surface area =

3

3

2

l

2

{\displaystyle {\frac {3{\sqrt {3}}}{2}}{l}^{2}}

### Subfacets

* 6 points (0D)
* 6 line segments (1D)
* 1 hexagon (2D)

### Radii

* Vertex radius:

l

{\displaystyle l}
* Edge radius:

3

2

l

{\displaystyle \frac{\sqrt{3}}{2}l}

### Vertex coordinates

The vertex coordinates of a regular hexagon of side 2 are:

* (±1,±√3)
* (±2,0)

### Related shapes

* Dual: Self dual
* Vertex figure: Line segment, length

3

{\displaystyle \sqrt{3}}

 (short diagonal)
* Long diagonal: Line segment of length 2

## See Also

t
0

{
6
}

{\displaystyle t\_0 \{6\}}

t
1

{
6
}

{\displaystyle t\_1 \{6\}}

t

0
,
1

{
6
}

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

t
0

{
3
}

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

t
1

{
3
}

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

t

0
,
1

{
3
}

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

t
0

{

6
5

}

{\displaystyle t\_0 \{\frac{6}{5} \}}

t
1

{

6
5

}

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

t

0
,
1

{

6
5

}

{\displaystyle t\_{0,1} \{\frac{6}{5} \}}
Minor planet

A **minor planet** is an astronomical object orbiting a star or stellar remnant that is not a planet nor an object that is exclusively a comet.

Minor planets encompass asteroids, dwarf planets, centaurs, and satellites of those objects. Dwarf planets are non-satellite minor planets which are in hydrostatic equilibrium, a trait that they share in common with planets. Asteroids are smaller objects that do not need to be in hydrostatic equilibrium that cannot clear their orbits of similarly sized objects. Centaurs are objects intermediate in size between asteroids and dwarf planets that typically pertain an unstable orbit and characteristics of asteroids and comets, some actually are considered very large comets.
Infinite-order hexagonal tiling

An **infinite-order hexagonal tiling** is a regular hyperbolic tiling in which an infinite amount of regular hexagons surround each vertex.

## See Also

{
6
,
2
}

{\displaystyle \{6,2\}}

{
6
,
3
}

{\displaystyle \{6,3\}}

{
6
,
4
}

{\displaystyle \{6,4\}}

{
6
,
5
}

{\displaystyle \{6,5\}}

{
6
,
6
}

{\displaystyle \{6,6\}}

{
6
,
7
}

{\displaystyle \{6,7\}}

{
6
,
8
}

{\displaystyle \{6,8\}}

{
6
,
∞
}

{\displaystyle \{6,\infty\}}

{
6
,

π
i

λ

}

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

{
2
,
∞
}

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

{
3
,
∞
}

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

{
4
,
∞
}

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

{
5
,
∞
}

{\displaystyle \{5,\infty\}}

{
6
,
∞
}

{\displaystyle \{6,\infty\}}

{
7
,
∞
}

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

{
8
,
∞
}

{\displaystyle \{8,\infty\}}

{
∞
,
∞
}

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

{

π
i

λ

,
∞
}

{\displaystyle \{\frac{\pi i}{\lambda},\infty\}}
Imaginary-order octagonal tiling

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

## See Also

Template:Variant Nav 8 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}\}}
Earth

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 → **Earth**

**Earth** is the third planet from the Sun. It is notable for being the currently only known object in the Universe with life, from the smallest and simplest micro-organisms to the largest whales to highly sophisticated and intelligent human beings. Earth sustains life, mainly because of special conditions that could allow a planet to potentially have life.

Earth sits in the habitable zone of our star, the Sun, which gives Earth just the right amount of heat and light for plants to photosynthesize and also allows water, a very important chemical for life, to exist in its liquid state. Earth also has an atmosphere that contains diatomic oxygen, which lifeforms also need to live. This atmosphere also has an ozone layer that absorbs most of the Sun's ultraviolet light, protecting complex lifeforms from forms of cancer. Earth's atmosphere is further protected by its magnetic field, which exists because of Earth's iron core.

As of right now, it is unknown if there are other planets that may sustain life as well. However, as technology continues to develop and aid with our research, we may be leaning towards yes as an answer.
Grape-class riftpod

The ***Grape*-class** **riftpod**is a type of extremely small and primitive vehicle (that is, in relation to many other vehicles of its kind) capable of traversing the Rifters' Realm. As its name implies, it is shaped like a grape, and is designed for occupation by a single humanoid being with a height anywhere from 1.4 to 2.1 meters. It is usually found throughout a portion of the Realm corresponding to a multiverse designated 1-6 by the cosmic entities that govern it, although it can also be occasionally found in parts of the Realm corresponding to multiverses adjacent to 1-6.

## History

The *Grape*-class riftpod was first designed by a small group of a few dozen or so multiversal explorers from a backwater portion of multiverse 1-6 who were trying to develop a quick and easy way for them to travel between universes. Needless to say they were never able to achive that goal, but they did end up becoming the first in their universe to discover the Rifters' Realm as well as develop the earliest version of the *Grape*-class. The blueprints for this vehicle class would then slowly spread across multiverse 1-6 over the course of hundreds of millions of years, being somewhat modified over time and eventually becoming the go-to vehicle when wanting to take a trip through the Rifters' Realm for whatever reason.

## Design

The modern design of the *Grape*-class is about 3.2 meters in its longest dimension, of which there are always three total. The majority of the vehicle's volume consists of the "passenger storage bay", in which said passenger is put in stasis for the duration of the trip. The 50-centimeter-long rift turbine located at the back of the vehicle has a SICO of about 4.1, which makes the average length of a trip between adjacent universes on the *Grape*-class around 10-20 years. Among the more advanced civilizations of multiverse 1-6 (of at least an intergalactic level of development), this is not considered to be a long travel time because advances in longevity render individuals effectively immortal.
Hexagonal hosohedron

A **hexagonal hosohedron** is a 3-dimensional polyhedron with six 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

{
6
,
2
}

{\displaystyle t\_0 \{6,2\}}

t
1

{
6
,
2
}

{\displaystyle t\_1 \{6,2\}}

t
2

{
6
,
2
}

{\displaystyle t\_2 \{6,2\}}

t

0
,
1

{
6
,
2
}

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

t

1
,
2

{
6
,
2
}

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

t

0
,
2

{
6
,
2
}

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

t

0
,
1
,
2

{
6
,
2
}

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

{
2
,
6
}

{\displaystyle \{2,6\}}

{
3
,
6
}

{\displaystyle \{3,6\}}

{
4
,
6
}

{\displaystyle \{4,6\}}

{
5
,
6
}

{\displaystyle \{5,6\}}

{
6
,
6
}

{\displaystyle \{6,6\}}

{
7
,
6
}

{\displaystyle \{7,6\}}

{
8
,
6
}

{\displaystyle \{8,6\}}

{
∞
,
6
}

{\displaystyle \{\infty,6\}}

{

π
i

λ

,
6
}

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

The **great dodecahedron**, with Bowers' acronym **gad**, is a regular, uniform 3-dimensional star polyhedron with pentagonal faces that make pentagrammic vertex figures and one of the Kepler-Poinsot polyhedra. It is the dual to the small stellated dodecahedron.

## Structure and Sections

### Subfacets

* 12 points (0D)
* 30 line segments (1D)
* 12 pentagons (2D)
* 1 great dodecahedron (3D)

## See also

* Polytope Wiki. "Great dodecahedron".
* Bowers, Jonathan. "Polyhedron Category 1: Regulars".

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

{
5
,
2
}

{\displaystyle \{5,2\}}

{
5
,
3
}

{\displaystyle \{5, 3\}}

{
5
,
4
}

{\displaystyle \{5,4\}}

{
5
,
5
}

{\displaystyle \{5,5\}}

{
5
,
6
}

{\displaystyle \{5,6\}}

{
5
,
7
}

{\displaystyle \{5,7\}}

{
5
,
8
}

{\displaystyle \{5,8\}}

{
5
,
∞
}

{\displaystyle \{5,\infty\}}

{
5
,

π
i

λ

}

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

Template:Variant Nav X frac 5 2
In-between Space

A theoretical 'space' that can exists outside of the current archverses, and only is contained by the highest cosmological collection. In theory, all quantum foam in reality is not as simple as just a material, given into the fact that it can bend space-time as well as warp the perception of size. So with every infinite possibility in the omniverse and beyond, quantum foam can also be thought of everything, even if it appears to be nothing. There is no space void of quantum foam.

With some type of matter being present everywhere in reality, even in a vacuum, we can assume that there are solo universes (not contained by a higher archverse) and solo multiverses, megaverses, and so on. This may be true for our universe, since we have no proof that our world exists in a multiversal dimension, or even exists in an omniverse at all. This could explain if/when, we discover the secrets beyond our person world.
Heptagonal dihedron

A **heptagonal dihedron** is a 3-D polyhedron with two heptagonal 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

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\}}
Ennealmverse

An **ennealmverse** is a universe that occupies 9-Dimensional Space.

As usual, ennealmverses 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.
Imaginary-order pseudogonal tiling

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

An **imaginary-order pseudogonal tiling** is a noncompact hyperbolic tiling related to the infinite-order apeirogonal tiling, but its faces and vertex figures are pseudogons, which are special kinds of apeirogon that tile hypercycles in a hyperbolic plane.

## See Also

{
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}\}}

{

π
i

λ

,
2
}

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

{

π
i

λ

,
3
}

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

{

π
i

λ

,
4
}

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

{

π
i

λ

,
5
}

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

{

π
i

λ

,
6
}

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

{

π
i

λ

,
7
}

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

{

π
i

λ

,
8
}

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

{

π
i

λ

,
∞
}

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

{

π
i

λ
1

,

π
i

λ
2

}

{\displaystyle \{\frac{\pi i}{\lambda\_1},\frac{\pi i}{\lambda\_2}\}}
Hexeract

A **hexeract** or **dodecapeton** is the 6-dimensional hypercube. It can be considered to be a prism with a penteract as the base. Its Bowers name is **ax**, and it can also be called a **geopeton**.

## Structure and Sections

As a penteractic prism, this is just two penteracts connected in 6-D space.

### Hypervolumes

* vertex count =

64

{\displaystyle 64}
* edge length =

192
l

{\displaystyle 192l}
* surface area =

240

l

2

{\displaystyle 240{ l }^{ 2 }}
* surcell volume =

160

l

3

{\displaystyle 160{ l }^{ 3 }}
* surteron bulk =

60

l

4

{\displaystyle 60{ l }^{ 4 }}
* surpeton pentavolume =

12

l

5

{\displaystyle 12{ l }^{ 5 }}
* surecton hexavolume =

l

6

{\displaystyle { l }^{ 6 }}

### Subfacets

* 64 points (0D)
* 192 line segments (1D)
* 240 squares (2D)
* 160 cubes (3D)
* 60 tesseracts (4D)
* 12 penteracts (5D)
* 1 hexeract (6D)
Hyperball

The hyper-ball (n-ball) is the space bounded by a hypersphere.

For n-dimensional Euclidean space

R

n

{\displaystyle \R^n}

 open n-ball

B
o
n

{\displaystyle B\_o^n}

 of radius *r* and center *c* is the set of all points of distance less than *r* from point *c*:

B
o
n

=

{

x
∈

R

n

d
(
x
,
c
)
<
r

}

{\displaystyle B\_o^n = \left\{ x \in \mathbb{R}^{n} | d(x,c) < r \right\} }

where

d
(
x
,
c
)

{\displaystyle d(x,c)}

 is euclidean metric for n-dimensional space

d
(
x
,
c

# i
1

n

(

x
i

−

c
i

)
2

{\displaystyle d(x,c)=\sqrt{\sum\_{i=1}^{n} (x\_i - c\_i)^2}}

.

For n-dimensional Euclidean space

R

n

{\displaystyle \R^n}

 closed n-ball

B
c
n

{\displaystyle B\_c^n}

 of radius *r* and center *c* is the set of all points of distance less than or equal to *r* from point *c*:

B
c
n

=

{

x
∈

R

n

d
(
x
,
c
)
≤
r

}

{\displaystyle B\_c^n = \left\{ x \in \mathbb{R}^{n} | d(x,c) \le r \right\} }

Examples:

* For 1-dimensional Euclidean space the 1-ball is an interval,
* For 2-dimensional Euclidean space the 2-ball is a disk,
* For 3-dimensional Euclidean space the 3-ball is a ball.
Faceted hexacosichoron

A **faceted hexacosichoron**, also known as an **icosahedral hecatonicosachoron**, is a regular star polychoron with 120 icosahedral cells. It is one out of ten Schläfli-Hess polytopes. Its dual is the small stellated hecatonicosachoron.

Its Bowers acronym is **fix**.

## External Links

* Polytope Wiki. "Faceted hexacosichoron".
* Bowers, Jonathan. "Category 1: Regular Polychora".

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

The **Huge Large Quasar Group** is a possible structure of 73 quasars is a large quasar group that measures about 4 billion light-years across. It was identified as the largest and the most massive known structure in the observable universe at its discovery. It has since been surpassed by the Hercules Corona Borealis Great Wall, which spans at over 10 billion light years.
Incomplete Verse

An **Incomplete Verse** is a Verse that, as the name implies, is not fully formed or complete in all senses of the word.

## **Definition**

What this means is that it probably lacks one or more of the essential components that usually make up a verse of its kind. Maybe it is formed by a space-time fabric as normal but there is nothing inside the space formed by its dimensions or maybe there are matter and energy in there, just no space where it is contained. Maybe there are just no laws of physics to govern the interactions between matter and energy in any way.

It might be lacking any of its components or all but one.

## **Classification**

A single Planet floating around directly on the Multiverse can be seen as an incomplete universe. Even a Galaxy or a Solar System could be seen that way, although an isolated galaxy that is, nonetheless, fully functioning and normal in every other way would most likely be seen as a very small Universe while a single Solar System will be somewhere in the middle, possibly seen as one or the other.

Such small universes can also be called Microverses, in opposition to Macroverses which are very large universes that end up existing at the same level as higher order verses.

It is not always easy to differentiate between an Incomplete Verse and a Microverse, with the fundamental difference being that a Microverse exists, works and looks like a normal universe, with the difference that it is usually much smaller in size and, definitely, not infinite; while an Incomplete Verse lacks one or more of the normal verse components but can otherwise be of any size. Actually an Incomplete Verse can be the size of a Microverse, a normal verse or even a Macroverse for its size is not a factor at all, only its composition.

## **Formation**

They can be the result of an interrupted process of universe formation, like a Big Bang that went wrong or, on the other end, what was left after a normal universe started to break apart through whatever process corresponded to its end but which was not fully completed. Maybe the Incomplete Verse is just a normal Verse in the process of a slow death, with its components being destroyed one by one.
Logical liquid

**Logical liquids** occur when truths are uncoupled from each other; for example, there may be chunks of the crystal that follow ZF+C, and chunks of the crystal that follow ZF¬C. In a logical liquid, omnipotence is possible; changing a fact in the liquid will only alter the facts that depends on it, so entities suspended in the logical liquid can safely act only on sections of the liquid that they themselves are not logically dependent on. Examples of logical liquids include the Outside.
Megaverse

A **Megaverse** is a collection of multiple different Multiverses, either a finite or infinite amount of them, usually each having different properties and interuniversal laws, such as different cosmic events being possible, such as Big Booms, etc.

A megaverse can be contained by a Gigaverse or a Teraverse, or other -verses in the metric hierarchy, but this eventually leads back up to the Archverse chain.

To inhabitants of a multiverse, other multiverses in the same megaverse can be referred to parallel multiverses, alternate multiverses, or simply other multiverses, depending on the degree of similarity between multiverses in the megaverse. The former two are multiversal analogues of altverses. Some civilisations call the Megaverse an Omniverse, since they haven't discovered the Gigaverse yet.

The most common form of Megaverses( wich are 5-dimensional) are stacked on top of each other in a 6-Dimensional space, with multiple being stacked on top of each other in one Gigaverse.
Imaginary number

An **imaginary number** is a complex number such that it is the product of a real number and the imaginary unit, the principal square root of negative one within the complex numbers, which is often written as i (j is often used in electrical engineering since I is used for current). The sum of a real number and an imaginary number is a complex number and the product of two imaginary numbers is a negative number.

The term "imaginary" for these numbers was coined as a derogatory term for these numbers as they were regarded as fictional or useless, but many applications for imaginary and complex numbers have since been found.

The complex line can be viewed as an object isomorphic to a Euclidean plane. The imaginary line is a line orthogonal to the real line that intersects it at 0 and complex numbers can be viewed as points on the complex plane or two dimensional vectors. Multiplying a complex number by a positive imaginary number would scale the vector by the absolute value of the imaginary number and rotate it 90 degrees counterclockwise and when multiplying any two complex numbers, the absolute values multiply and the arguments add.

More generally, an "imaginary number" could refer to the product of a real number and any element of a basis of hypercomplex numbers that is not the identity element one. Hypercomplex numbers are distributive unital algebras over the field of real numbers. For instance, the quaternions have three principal imaginary units i, j, and k that satisfy i2 = j2 = k2= ijk = -1 and are analogous to the imaginary unit in the complex numbers. The multiplicative group of the elements of the basis of quaternions and their additive inverses is nonabelian and therefore multiplication of quaternions is noncommutative.

## References

1. ↑ https://gallica.bnf.fr/ark:/12148/btv1b86069594/f464.item.zoom
Snacktime

**Snacktime** is a Hartlanian children's television magazine programme developed by Charlotte Andjersson and Rose Dayson. Airing from 10 September 1994 to 6 June 2009, it ran for fifteen series and over 600 episodes.

The series follows the adventures of Miss Lilyflower, a schoolteacher who navigates the fictional town of Connaissance.

## Synopsis

Set inside the fictional city of Connaissance, the series follows the adventures of Miss Lilyflower, a playgroup teacher who loves nothing more than inviting their friends to “snacktime”. She s usually accompanied by one or multiple helpers. The featured snack is *always* a healthy food, with the exception of some specials which are not intended to be educational.

## Format

Episodes usually open up with Miss Lilyflower and her helper(s) presenting a mock chat show titled Snacktime, in front of both their pupils and the viewers at home. The first two minutes are dedicated to a specific healthy snack which later becomes prevalent in the episode, before it cues to the opening titles. Afterwards, it cuts to an exterior shot of the playgroup and shows a main character in an everyday environment. The series constantly switches back-and-forth between a sitcom-style main plot and a mock talk show.

There have been several “helpers” of Miss Lilyflower, or presenters: Pamela “Pumpky” Croteau (1994-1998; 2000-2009), Eric Hecker (1999-2006), Deborah Abarough (2004-2006), and Lorenzo “Enzo” Mularoni (2007-2009).

## History and production

Wanting to shake things up for the twenty-fourth series of Playtime in 1992, executive producer Charlotte Andjersson decided to commission a five-minute short entitled Snacktime. Her belief was that it was essential for children to learn about nutrition, something she believed wasn't being taught properly. She tasked the show's curriculum coordinator, Dr. Johanna Fouquer to write the educational elements. The segment had Andjersson voicing both Miss Lilyflower and Pumpky, both puppet characters. The short proved to be a hit with viewers and as a result, it was brought back as a recurring segment.

Around the same time, network executives were looking to commission a spin-off aimed at a slightly older demographic. One such proposal, entitled Schooltime, intended to prepare children for school. Charlotte Andjersson disliked this idea, as she believed a series about school might teach children “unrealistic expectations”. They compromised and had the show partially take place in a school.
Infinite-order pentagonal tiling

An **infinite-order pentagonal tiling** is a regular hyperbolic tiling in which an infinite amount of regular pentagons surround each vertex.

## See Also

{
5
,
2
}

{\displaystyle \{5,2\}}

{
5
,
3
}

{\displaystyle \{5, 3\}}

{
5
,
4
}

{\displaystyle \{5,4\}}

{
5
,
5
}

{\displaystyle \{5,5\}}

{
5
,
6
}

{\displaystyle \{5,6\}}

{
5
,
7
}

{\displaystyle \{5,7\}}

{
5
,
8
}

{\displaystyle \{5,8\}}

{
5
,
∞
}

{\displaystyle \{5,\infty\}}

{
5
,

π
i

λ

}

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

{
2
,
∞
}

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

{
3
,
∞
}

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

{
4
,
∞
}

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

{
5
,
∞
}

{\displaystyle \{5,\infty\}}

{
6
,
∞
}

{\displaystyle \{6,\infty\}}

{
7
,
∞
}

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

{
8
,
∞
}

{\displaystyle \{8,\infty\}}

{
∞
,
∞
}

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

{

π
i

λ

,
∞
}

{\displaystyle \{\frac{\pi i}{\lambda},\infty\}}
Imaginary-order hexagonal tiling

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

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

## See Also

{
6
,
2
}

{\displaystyle \{6,2\}}

{
6
,
3
}

{\displaystyle \{6,3\}}

{
6
,
4
}

{\displaystyle \{6,4\}}

{
6
,
5
}

{\displaystyle \{6,5\}}

{
6
,
6
}

{\displaystyle \{6,6\}}

{
6
,
7
}

{\displaystyle \{6,7\}}

{
6
,
8
}

{\displaystyle \{6,8\}}

{
6
,
∞
}

{\displaystyle \{6,\infty\}}

{
6
,

π
i

λ

}

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

{
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}\}}
Extended real line

The **extended real line** is an infinite one-dimensional shape comprising the Euclidean line, but with an extra points added at both ends. These two points are called {∞} and {-∞}, and are both distinct point boundaries of the extended real line. Because of this, it is topologically equivalent to a line segment.
Hexadecagon

A **hexadecagon** is a two-dimensional polygon with sixteen edges. Its Bowers acronym is **hed**.

## Structure and Sections

The regular hexadecagon has equal edges with each angle being 157.5 degrees.

* vertex count =

16

{\displaystyle 16}
* edge length =

16
l

{\displaystyle 16 l}
* surface area =

4

(

1

2

2

(

2

2

)

)

l
2

{\displaystyle 4 \left( 1 + \sqrt{2} + \sqrt{ 2 \left( 2 + \sqrt{2} \right) } \right) l^2}

## See Also

t
0

{
16
}

{\displaystyle t\_0 \{16\}}

t
1

{
16
}

{\displaystyle t\_1 \{16\}}

t

0
,
1

{
16
}

{\displaystyle t\_{0,1} \{16\}}

t
0

{
8
}

{\displaystyle t\_0 \{8\}}

t
1

{
8
}

{\displaystyle t\_1 \{8\}}

t

0
,
1

{
8
}

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