recursal/Fanatic-Fandom huggingface dataset:
Complex line

The **Argand plane** or **complex line** is the space made from considering all points that can be labelled with one complex number; this gives it a complex dimension of 1. Comtela exist as regular subsets of the complex line.

## Embedding in the Euclidean plane

The complex line can be embedded in the Euclidean plane by considering each complex coordinate to correspond to two real coordinates; the typical way to do this is

x
(
z
# )
Re
⁡
z

{\displaystyle x(z) = \operatorname{Re} z}

y
(
z
# )
Im
⁡
z

{\displaystyle y(z) = \operatorname{Im} z}

The inverse of this is simply

z
(
x
,
y
# )
x
i
y

{\displaystyle z(x,y) = x + iy}

This embedding means that the complex line is often called the complex plane, though strictly that refers to the space made from pairs of complex numbers.
Hollowverse

A Hollowverse (or Hollow Universe) is a Universe, if we can even call it that, which is an empty shell. Its ontological barrier is the only existing thing, which appears to be a bubble separating it from interdimensional nothingness.

## Info

Few know in fact. It is an unknown verse for many species present in many universes, perhaps it is because it is meaningless to enter into it since there is nothing in it, either that or what causes hollowverses to be created. One possible candidate is universes going under heat death.
Flat universe

A **flat universe** is a universe with any number of dimensions that has zero curvature. The density parameter

Ω

{\displaystyle \Omega}

, the ratio between the density of the universe and the critical density of the universe is equal to 1 in a flat universe. If the density parameter was greater than 1, it would be a hyperspherical, positively curved closed universe. If it was less than 1, then it would be a hyperbolic, negatively curved open universe.

## Structure

Flat universes are defined to have zero curvature, while staying a relatively constant shape (according to general relativity, a massive object actually distorts spacetime, causing gravity). The universe's space may globally take on the form of a Euclidean space, as it is flat everywhere. The shape of a universe including the temporal dimensions, the continuum of space and time, can be modeled as a Minkowski space with a signature determined by the number of spatial and temporal dimensions.

A flat universe will typically be infinite in size unless it has some borders or has some closed topology despite its space itself being flat, such as a toric, tubic or Klein bottle-shaped universe.

## Life cycle

Like all naturally created universes, a flat universe begins its life with a "Big Bang" and will continually expand throughout its life. However, unlike a closed universe, which expands from a infinitesimally small center point (known as the singularity or protoverse), open and flat universes start off as an extremely dense, hot, and curved but still infinite space, and regions that would eventually become Hubble volumes and/or googological regions are very compact and small.

Expansion will then slow down and the universe will cool down, and over the course of billions of years, galaxies, stars and planets (that *may* have life) may form.

The ultimate fate of the universe depends on the shape of the universe and the type of dark energy throughout the universe. Flat universes with a positive cosmological constant will continually will expand forever, but the expansion will decrease over time, it's growth and temperature asymptotically approaching zero in a Big Freeze scenario or will expand while going into a state of maximum entropy and matter dilutes, this scenario is known as Heat death.

Flat universes with negative phantom energy on the other hand, will either reaccelerate, soon expanding faster than light and overwhelming the fundamental forces and causing a "Big Rip". These three possible fates are shared with open universes. Closed universes on the other hand, go out with a Big Crunch.

## See Also

* Open universe - A universe with constant negative curvature, and is in the shape of a hyperbolic space
* Closed universe - A universe with constant positive curvature, and is in the shape of a hypersphere

## References

* https://en.wikipedia.org/wiki/Big\_Rip
* https://en.wikipedia.org/wiki/Heat\_death\_of\_the\_universe
* https://en.wikipedia.org/wiki/Shape\_of\_the\_universe
* https://en.wikipedia.org/wiki/Norm\_(mathematics)
Disk

A **disk** is a two-dimensional shape built from the solid interior of a circle.

## Structure and Subfacets

The disk is composed of a single curved edge. Its sections look like a point that expands to a line segment before shrinking back.

### Hypervolumes

* edge length =

π
l

{\displaystyle \pi l}
* surface area =

π
4

l
2

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

### Subfacets

* 1 circle (1D)
* 1 disk (2D)

### Equations

The edge of a disk of radius

r

{\displaystyle r}

, centered at the origin, can be given by the equation

x
2

y
2

=

r
2

{\displaystyle x^2 + y^2 = r^2 }

.

### Notations

* Toratopic Notation:

(
)

{\displaystyle ()}
* Tapertopic notation:

2

{\displaystyle 2}

## Coordinate system

The coordinate system based on the disk is called polar coordinates. Its two parameters are

r

{\displaystyle r}

, the radius of the circle, and

θ

{\displaystyle \theta}

, the angle from the positive x-axis.
Eris

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 → **Eris**

## Climate

### Temperature

42.5 K

**Eris** is the most massive and second-most voluminous minor planet and dwarf planet in the Solar System.

Due to its large mass, it was initially called the Solar System’s “tenth planet” as Pluto, a less massive object, was considered a planet at the time. After the International Astronomical Union defined the terms “planet” and “dwarf planet”, Eris and Pluto were soon classified as dwarf planets.

Eris’ orbit has a relatively high orbital eccentricity compared to Kuiper belt objects and is a member of the scattered disc. Eris has one known moon called Dysnomia.
Gigaversal Serial Bus

A **gigaversal serial bus** is a type of timeline organisation used by gigaversal civilisations in high-civ regions, and part of the core insight that lets civilisations advance past the megaversal level onto the archverse chain. The problem with standard gigaversal time travel is that two megaverses with time travel occurring independently to each other are hashed into each other; a tiny change in one set of timelines leads to a large change in the other set of timelines due to both of them sharing the same underlying timeline structures in the gigaverse.

Primitive gigaversal civilisations often solve this by declaring one cohort of megaverses the canonical cohort and allowing the others to fluctuate ~randomly to take whatever shapes are required in order to support industrial activity in the canonical cohort, often being destroyed by metamesonium and then replaced with clean megaverses when the timelines become too chaotic even compared. This is a direct extension from their nature as a megaversal civilisation, where their megaverse of origin is the canonical and only megaverse.

However, this approach has limits; eventually, a civilisation will want to expand onto these arbitrary megaverses, and finds themselves more overconstrained and unable to expand further.

To solve this, civilisations use arhadalite in order to maintain the independence of timeline families. Changes to a megaverse with arhadalite will randomise corresponding pieces of arhadalite, though those pieces of arhadalite are not necessarily elsewhere in the same gigaverse, and may well be significantly less real. This means that, regardless of intragigaversal timeline transmission, timelines can remain dependent only on their arhadalite which is independent of arhadalite elsewhere. Due to each megaverse cohort being arranged alongside the same piece of arhadalite in series, this procedure is known as connecting to the gigaversal serial bus.

Since arhadalite spans other archverses, this seems like it can be a useful way for civilisations to ascend the archverse chain, though in practise hashing and mixed reality levels mean that rangefinders are more reliable for most cases at the teraversal level; this procedure serves mostly for getting to a level where rangefinders can be employed at all.
Imaginary-order pentagonal tiling

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

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

## 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
,

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}\}}
Elliptical galaxy

**Elliptical galaxies** are a type of galaxy that are round or oval in shape and are mostly made up of older stars; it is believed that many galaxy collisions end up creating elliptical galaxies, and that eventually they will become more common as the universe ages. They vary in size; dwarf elliptical galaxies can be made up of just a few million stars, while the largest of them can have trillions.

Elliptical galaxies make up approximately 10-15% of large galaxies in the Virgo Supercluster.

Elliptical galaxies are designated with the type E*n*, with *n* equal to:

10
×
(
1
−

b
a

)

{\displaystyle 10\times (1-{\frac {b}{a}})}

where

a

{\displaystyle a}

 is the galaxy's major axis and

b

{\displaystyle b}

 is its minor axis. In general, elliptical galaxies range from E0 to E7. Beyond E7, an instability called the firehose instability occurs which causes the galaxy to buckle up and become rounder. The most common type of elliptical galaxy is E3.

Well-known elliptical galaxies in our universe include IC 1101 (the largest galaxy we know to this day), M87, and Maffei 1.
Gidpathidy

720 decagrams

3600 squares

2400 hexagons

120 rhombicosahedra

120 great dodekicosahedra

120 great rhombicosidodecahedra

A **great dipentary trishecatonicosadishecatonicosachoron** is a uniform polychoron in the great dipentary trishecatonicosachoron regiment with 720 vertices, 3600 edges, 10560 faces, and 600 cells.

Its Bowers acronym is **gidpathidy**.

## Structure and Sections

The gidpathidy is in the great dipentary trishecatonicosachoron (**gidipthi**) regiment. This means that it has the same edge arrangement and edge count as gidipthi. Being in the same regiment as gidipthi also implies that the relationship between the circumradius and edge length of a gidpathidy is the same as gidipthi's, which is

l

4
−

5

{\displaystyle l\sqrt{4-\sqrt{5}}}

 for edge length

l

{\displaystyle l}

.

The vertex figure of a gidpathidy is a variant of **pentagonal podium**.

### Hypervolumes

* vertex count =

1440

{\displaystyle 1440}
* edge length =

7200
l

{\displaystyle 7200l}

### Subfacets

* 1440 points (0D)
* 7200 line segments (1D)
* 1440 pentagrams (2D)
* 2400 triangles (2D)
* 720 decagrams (2D)
* 3600 squares (2D)
* 2400 hexagons (2D)
* 120 small stellated dodecahedra (3D)
* 120 icosahedra (3D)
* 120 rhombicosahedra (3D)
* 120 great dodekicosahedra (3D)
* 120 great rhombicosidodecahedra (3D)
* 1 great dipentary trishecatonicosadishecatonicosachoron (4D)

## See Also

* Polytope Wiki. "Great dipentary trishecatonicosidishecatonicosachoron".
* Bowers, Jonathan. "Category 22: Gidipthi Regiment".

## References

1. ↑ http://www.polytope.net/hedrondude/gidipthi.htm
Gigaverse

The **Gigaverse** is the fourth nested level of the metric -verse series and the lowest-level archverse. This archverse contains a finite or infinite amount of megaverses, which are the third nested level. It is contained by the Teraverse, which is an finite or infinite set of gigaverses.

At scales higher than Gigaverse, the dimensionality becomes hard to measure. This is caused by the fractal nature of a Gigaverse. The most common amount of dimensions for gigaverses are between 6-Dimensional and 11-Dimensional
Elementary fermion

An **elementary fermion** is a particle with a half-integer spin which can not be further decomposed into smaller particles. There are 96 elementary fermions, sorted into three generations which each have similar properties to the previous but with a greater mass.

Due to the spontaneous symmetry breaking by the Higgs field, normal elementary fermions are typically found in their left-handed forms and antimatter elementary fermions are typically found in their right-handed forms.

## Quarks

Quarks come in two categories: up-type quarks and down-type quarks. The up-type quarks include the up quark, the charm quark, and the top quark. The down-type quarks include the down quark, the strange quark, and the bottom quark.

The left-handed up-type quarks have an electric charge of +2⁄3 and a weak isopin of +½, and the left-handed down-type quarks have an electric charge of -1⁄3 and a weak isospin of -½. The right-handed up-type quarks have an electric charge of +2⁄3, and the right-handed down-type quarks have an electric charge of -2⁄3, with both having a weak isospin of 0.

Each quark can come in six different colours (red, green, blue, antired, antigreen and antiblue), with normal quarks coming in the normal colours and antiquarks coming in the anticolours. These colours dictate how the quark interacts by the strong nuclear force. Because of how the strong force behaves over long distances, quarks can not be isolated, and must come bound in colourless hadrons.

## Leptons

Leptons also come in two categories: electron-type leptons (the "down" leptons) and neutrino-type leptons (the "up" leptons). The electron-type leptons include the electron, the muon, and the tauon. The neutrino-type leptons include the electron neutrino, the muon neutrino, and the tauon neutrino.

The left-handed electron-type leptons each have an electric charge of -1, and a weak isospin of -½. The left-handed neutrino-type leptons each have no electric charge, and a weak isospin of +½. The right-handed electron-type leptons have an electric charge of -1, and the right-handed neutrino-type leptons have no electric charge, with both having a weak isospin of 0.

Leptons come in two "colours" (white and black), with normal leptons being white and antileptons being black, both of which are colourless and do not interact with the strong force, so they can be isolated and need not exist in bound states.

Because right-handed neutrinos have no colour, charge or weak isospin, they do not interact by any of the fundamental forces except for gravity.
Extended ray

An **extended ray** is a one dimensional shape similar to a ray, but on the extended real line rather than the Euclidean line. This means that it is a ray with one extra point added, corresponding to a distinct point at either positive or negative infinity, making a boundary on the other end of the ray. Because of this, it is topologically equivalent to a line segment.
Hercules–Corona Borealis Great Wall

Universe → **Hercules–Corona Borealis Great Wall**

The Hercules-Corona Borealis Great Wall is the largest detected structure in our observable universe. This structure has not been seen however, and was only detected by mapping gamma ray bursts. The readings show 14 similar bursts that have redshifted. If this is true then the structure would be 10 billion light years long.

This structure, if it is actually that big, would cancel out many theories about the evolution of this universe. We are detecting these gamma ray bursts 10 billion light years away. Meaning these structure formed 10 billion years ago. If this is true then many new theories would have to be proposed in order to find out why this massive structure formed in this time.
Haumea

Depiction of Haumea with its ring

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 → Kuiper belt → **Haumea**

**Haumea** is a dwarf planet that resides in our Solar System's Kuiper belt past Neptune. It is considered to be a very unusual object, as it has many qualities that make it stand out from most of the dwarf planets.

For a start, Haumea takes the shape of a tri-axial ellipsoid. Most objects like Haumea that rotate quickly take on the shape of an oblate spheroid (for reference, Saturn or Vega), but Haumea rotates so fast that it distorts even further into a tri-axial ellipsoid.

Haumea also pertains a very large red spot on its surface very rich in minerals, organic compounds and crystalline water ice. The latter, which composes most of Haumea's surface, is unusual as Haumea (along with other objects with a similar surface, such as Pluto's moon Charon) is well under the temperature needed to form crystalline water (-163 °C), at -223 °C, where it should be amorphous ice, not to mention the fact that solar radiation would have made crystalline ice unstable. It is currently unknown how Haumea resurfaces its ice.

In 2017, a ring was been discovered around Haumea. This is the first ring system found around a Trans-Neptunian object.

Haumea has two known moons. Their names are **Hi'iaka** and **Namaka**.

## References

1. ↑ https://web.archive.org/web/20090923170519/http://www.news.com.au/story/0%2C27574%2C26081101-23109%2C00.html
2. ↑ https://arxiv.org/abs/astro-ph/0601618
3. ↑ https://doi.org/10.1038%2Fnature24051
Infinite-order heptagonal tiling

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

## See Also

Template:Variant Nav 7 X

{
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\}}
Elliptic curve

Elliptic curves over the real numbers '"`UNIQ--postMath-00000001-QINU`"' (Figure 1, left) and '"`UNIQ--postMath-00000002-QINU`"' (Figure 2, right).

## Subfacets

### Edges

1 **elliptic curve**

An **elliptic curve** defined over a field

K

{\displaystyle K}

 (such as the rational numbers

Q

{\displaystyle \mathbb{Q}}

, real numbers

R

{\displaystyle \R}

, complex numbers

C

{\displaystyle \mathbb{C}}

, or

p

{\displaystyle p}

-adic numbers

Q

p

{\displaystyle \mathbb {Q}\_p}

) is a nonsingular, projective, genus-one cubic curve of two variables. Assuming that the field does not have a field characteristic of 2 or 3, like

Q

{\displaystyle \mathbb{Q}}

,

R

{\displaystyle \R}

, and

C

{\displaystyle \mathbb{C}}

, every elliptic curve can be defined with the Weierstrauss equation

y
2

=

x
3

a
x
b

{\displaystyle y^2=x^3+ax+b}

where

a

{\displaystyle a}

 and

b

{\displaystyle b}

 are elements of

K

{\displaystyle K}

.

As elliptic curves are nonsingular, they do not have any cusps, self-intersections, or isolated points.

Elliptic curves are not ellipses.
Femtotechnology

**Femtotechnology** is technology that operates on the scale of femtometres, around 10-15 m. This is estimate equal to the size of atomic nucleus, so using femtotechnology requires the ability of controlling hadrons.

It was unknown for attotechnology as we don't know what quarks really do in a clear way.
False Author Authority

*Not to be confused with Actual Author Authority.*

**False Author Authority** is a type of magic used by Reality Warpers that allow them to alter existence on a low to nigh omnipotent level. The Aspect Lords are the most common users of this magic, with The Infinite Madness coming in at second.

## **Properties/Info**

There isn't really much to say about False Author Authority other than that it comes close to Omnipotence on the power strength hierarchy, and it would be the strongest if we didn't count omnipotence at all.

The difference between this power and Reality Warping is that this power can be accessed by mortals or weaker entities using tools or weapons such as The Book of Beginning and End, which is a large book with every moment of every possible universe and every possible timeline's details in it, with an infinite amount of pages infinitely packed into one space, making it immovable, which constantly updates itself when things happen.

However, users of False Author Authority do not require objects to use the power.
Ericka streets first appearance on Zinkle

Kiki: Meet the new girl on Zinkle, she's the legendary Kuboian Ericka Ilizabeth Streets!

Ericka: \*literally bouncing up and down\* Hiiiiii!!!

Kiki: And she voices Stella and Roxy in Winx Club!

Ericka: I sure do!

Kiki: Speaking of Winx Club, it's coming up next on Zinkle on HBC!

Ericka: if you desire you can become one of our bunch...
Les Fashionistas Intro

Sung by Ericka Streets.

Come on, girl

Buckle up for the ride

Let's take on the world

And take on it with pride

Take the world on with might,

It's high-time we do this right

When you're takin' on a new school

You gotta play by your own rules

And then you find out,

what it's all about

Summer's gone with the wind

That's when the real fun begins

And that ain't no lie

It's great at Valley View High!
Hexadekasphere

A **hexadekasphere** is a 16-dimensional surface produced by finding the set of all points that are an equal distance from another point in 17-dimensional space. Because it is curved, it is often represented embedded in 17-dimensional space. A hexadekasphere is the shape of the exterior of a heptadekorb. It is the 16-dimensional hypersphere.
4-dimensional orthogonal symmetry

**4-dimensional orthogonal symmetry** (O(4)) is the set of all rotations and rotations followed by reflections in four-dimensional space; members of this group remain identical under all rotations and reflections. It is the symmetry group of the gongol, and the glome under its standard embedding in the flune.

This can also be expressed as the set of all 4×4 matrices that have their transpose equal to their inverse. This means their determinants are either 1 or -1; the matrices with determinant 1 are rotations (and correspond to the 4-dimensional special orthogonal symmetry group), and the matrices with determinant -1 are rotations followed by reflections.
Gonggong

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 → **Gonggong**

## Physical Structure

### Diameter

1535 km

**Gonggong**, provisional designation **2007 OR10**, is a very large dwarf planet orbiting in the Scattered disc of our Solar system. It was originally nicknamed "Snow White" by its discoverers because of its presumed white color (as it would've been very bright to be detected), but it turned out to be one of the reddest objects in the Solar system, so the name was dropped.

Gonggong has one satellite called **Xiangliu**.
Hyperbolic plane

A **hyperbolic plane** is an infinitely large 2-dimensional space that follows hyperbolic geometry, and has a constant negative curvature throughout the space. It is a complete and smooth surface.

It is impossible to embed a complete hyperbolic plane in a Euclidean 3-dimensional space while preserving distance by Hilbert’s theorem.

## References

* https://en.wikipedia.org/wiki/Hilbert%27s\_theorem\_(differential\_geometry)
Glome

A **glome** is a 3-dimensional surface produced by finding the set of all points that are an equal distance from another point in 4-dimensional space. Do to it being curved, it is often represented embedded in 4-dimensional space. A glome is the shape of the exterior of a gongol. It is the 3-dimensional hypersphere.

## Embeddings

### ℝ4

A glome can be defined parametrically using the parameters

ψ

{\displaystyle \psi}

,

θ

{\displaystyle \theta}

 and

ϕ

{\displaystyle \phi}

by

x
(
ψ
,
θ
,
ϕ
)

=
r
sin
⁡
ψ
sin
⁡
θ
sin
⁡
ϕ

y
(
ψ
,
θ
,
ϕ
)

=
r
sin
⁡
ψ
sin
⁡
θ
cos
⁡
ϕ

z
(
ψ
,
θ
,
ϕ
)

=
r
sin
⁡
ψ
cos
⁡
θ

w
(
ψ
,
θ
,
ϕ
)

=
r
cos
⁡
ψ

{\displaystyle {\begin{aligned}x(\psi ,\theta ,\phi )&=r\sin \psi \sin \theta \sin \phi \\y(\psi ,\theta ,\phi )&=r\sin \psi \sin \theta \cos \phi \\z(\psi ,\theta ,\phi )&=r\sin \psi \cos \theta \\w(\psi ,\theta ,\phi )&=r\cos \psi \\\end{aligned}}}

Where r is a constant defining the radius of the glome. Squaring all of these and adding them together gives the cartesian form of the glome with radius r,

x

2

y

2

z

2

w

2

−

r

2

=
0

{\displaystyle x^{2}+y^{2}+z^{2}+w^{2}-r^{2}=0}

### ℍ1

The glome can also be embedded in a quaternion coordinate space using the parameters

ψ

{\displaystyle \psi}

,

θ

{\displaystyle \theta}

 and

ϕ

{\displaystyle \phi}

 by

q
(
ψ
,
θ
,
ϕ
)

=
r

e

(

(

cos
⁡
θ

)

i

(

sin
⁡
θ
cos
⁡
ϕ

)

j

(

sin
⁡
θ
sin
⁡
ϕ

)

k

)

ψ

{\displaystyle {\begin{aligned}q(\psi ,\theta ,\phi )&=r{e}^{\left(\left(\cos \theta \right)i+\left(\sin \theta \cos \phi \right)j+\left(\sin \theta \sin \phi \right)k\right)\psi }\\\end{aligned}}}
Hyperrealmverse

A **hyperrealmverse** is a verse that exists in a space that is a Hyperrealm, meaning that it exists with 4 or more dimensions.

The following hyperrealmverses have pages on this wiki:

* 4 dimensions: Fluneverse

* 5 dimensions: Pentrealmverse
* 6 dimensions: Hexealmverse
* 7 dimensions: Heptealmverse
* 8 dimensions: Octealmverse
* 9 dimensions: Ennealmverse
* 10 dimensions: Decealmverse
* 11 dimensions: Hendecealmverse
* 12 dimensions: Dodecealmverse
* 13 dimensions: Tridecealmverse
* 14 dimensions: Tetradecealmverse
* 15 dimensions: Pentadecealmverse
* 16 dimensions: Hexadecealmverse
* Infinite dimensions: Omegealmverse
Elemental complex polytope naming scheme

The **elemental complex polytope naming scheme** is a method for naming complex polytopes in any number of dimensions.

The prefixes used are named after chemical elements on the periodic table, and an element's atomic number corresponds to the Shephard-Todd number (ST) of the reflection group of the polycomtope.

## References

1. ↑ http://verse-and-dimensions.wikia.com/wiki/User\_blog:Holomanga/Complex\_Polytopes
2. ↑ https://en.wikipedia.org/wiki/Complex\_reflection\_group#List\_of\_irreducible\_complex\_reflection\_groups
Gammaverse

A **Gammaverse**, aka **GR**Verse or **G**amma **R**ay verse, is an extremely dangerous universe. In there all energy is instantly turned into gamma rays by some unknown force. This makes life as we know it almost impossible to exist. Black holes that emit gamma rays have their rays powered up to a thousand-fold to a billion-fold.

The gamma rays here are unbelievably energetic (much more than the ultra-high-energy gamma rays) to such a point that each photon can be said to contain an infinite amount of energy without creating a black hole singularity for some reason. Or maybe each photon is a singularity that, for some reason, acts in a different way than normal black holes and more similarly to normal, less energetic photons. This leads to extreme effects that brake the laws of physics and allows them to be able to do things like exceeding the speed of light or even being able to escape the universe and, possibly, affect other universes close by in the multiversal space.

## Gammaverse Phase

In many universes, during the final moments of their existence, the contraction of the universe into a singularity (a Big Crunch event) results in photons naturally being blueshifted into gamma rays.
Class K star

A **Class K star** is the sixth-brightest type of main sequence star. They are typically colored yellow-orange or orange. They make up roughly 12% of all main-sequence stars.

A typical Class K star has a mass of 0.6 (0.45 to 0.8) solar masses, a radius of 0.8 (0.7 to 0.96) solar radii, a luminosity of 0.3 (0.08 to 0.6) solar luminosities, a surface temperature of 4,450 K (3,700 K to 5,200 K), and a lifespan of 50 to 100 billion years.

With their extremely long lifespans and acceptable brightness, it is very likely that many Class K stars have life-bearing planets, and many exoplanets have been discovered around stars of this class.

## Properties of K-type main sequence stars

Compared to stars like the Sun, K-type stars are generally notably smaller, cooler, less massive, and less luminous. Their small size and cooler temperatures are factors towards them being alternatively known as "**orange dwarfs**". The most luminous Class K stars are about two thirds the luminosity of the Sun while the least luminous are less than a tenth of the Sun's luminosity.

The spectra of Class K stars are characterized by strong sodium, neutral metal (e.g. Si I, Mn I, Fe I), and singly ionized metal (Ca II, Fe II) lines and extremely weak to nonexistent hydrogen lines. Lines of diatomic molecules such as TiO and CO are often present in cooler Class K stars.

## See Also

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

## References

* Cram, Lawrence E., and Leonard V. Kuhi. *FGK Stars and T Tauri Stars*. NASA, 1989.
* Mamajek, E., *A Modern Mean Dwarf Stellar Color and Effective Temperature Sequence*. 2019
Hexagonal dihedron

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

{
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}\}}

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\}}

{
0
,
2
}

{\displaystyle \{0,2\}}

{
1
,
2
}

{\displaystyle \{1,2\}}

{
2
,
2
}

{\displaystyle \{2,2\}}

{
3
,
2
}

{\displaystyle \{3,2\}}

{
4
,
2
}

{\displaystyle \{4,2\}}

{
5
,
2
}

{\displaystyle \{5,2\}}

{
6
,
2
}

{\displaystyle \{6,2\}}

{
7
,
2
}

{\displaystyle \{7,2\}}

{
8
,
2
}

{\displaystyle \{8,2\}}

{
∞
,
2
}

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

{

π
i

λ

,
2
}

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

A **hexagonal cupola** is a three-dimensional polyhedron created from taking the cupola of a hexagon, making it a segmentohedron of a hexagon and a dodecagon.

The regular form of a hexagonal cupola, with all of its edges being of equal length and its faces regular polygons, is flat.

## Structure and Sections

### Subfacets

* 18 points (0D)
* 30 line segments (1D)
* 6 triangles (2D)
* 6 squares (2D)
* 1 hexagon (2D)
* 1 dodecagon (2D)
* 1 **hexagonal cupola** (3D)

### Hypervolumes

* vertex count =

18

{\displaystyle 18}
* edge length =

30
l

{\displaystyle 30l}
* surface area =

(
12
6

3

)

l
2

{\displaystyle (12+6\sqrt{3})l^2}
* surcell volume =

0

l
3

{\displaystyle 0l^3}

## See Also

{
2
}

t

0
,
1

{
2
}

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

{
3
}

t

0
,
1

{
3
}

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

{
4
}

t

0
,
1

{
4
}

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

{
5
}

t

0
,
1

{
5
}

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

{
6
}

t

0
,
1

{
6
}

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

An **incipiverse** is a verse in which the laws of physics or some part thereof, like some specific property of the verse, becomes less definite with distance. The simplest form of incipiverse is the **spherical incipiverse**, in which there is a single fixed center of certainty and things become more and more uncertain the further away from it they are.

One common source of spherical incipiverses are simulations where position is defined with a fixed precision relative to the origin. If the position of a particle is stored as a 32 floating point number, then at around 107 units from the origin position has an uncertainly of one unit and at around 1023 units position is almost meaningless.

## References

1. ↑ http://en.wikipedia.org/wiki/Single-precision\_floating-point\_format
Infinite-order square tiling

The infinite-order square tiling is a regular hyperbolic tiling formed from squares joining a countably infinite number to a vertex.

This tiling can have a two-colouring on the squares, leading to the 44∞ loop group.

## See Also

{
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\}}

{
4
,
2
}

{\displaystyle \{4,2\}}

{
4
,
3
}

{\displaystyle \{4,3\}}

{
4
,
4
}

{\displaystyle \{4,4\}}

{
4
,
5
}

{\displaystyle \{4,5\}}

{
4
,
6
}

{\displaystyle \{4,6\}}

{
4
,
7
}

{\displaystyle \{4,7\}}

{
4
,
8
}

{\displaystyle \{4,8\}}

{
4
,
∞
}

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

{
4
,

π
i

λ

}

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

Template:Variant Nav infty 4
Hypercycle

A **hypercycle** is a curve homeomorphic to a straight line within a hyperbolic plane such that for all points in the curve, they are some constant distance

r

{\displaystyle r}

 from a straight line called its **axis**. The distance

r

{\displaystyle r}

 is called the **radius** of the hypercycle. A hypercycle of radius 0 is a straight line.

Given a straight line L and a point P not on L, one can construct a hypercycle H with a radius greater than 0 that passes through P. L divides the plane into two disjoint open half-planes. A point Q is on the same side of L as P if they are both elements of the same open half-plane. The perpendicular distance of a point Q to L is the distance between Q and the point in L of the shortest distance to Q. The hypercycle defined by L and P is the set of all points Q on the same side as P with a perpendicular distance to L equal to that of P’s.

Just like a circle in the hyperbolic plane, the limit of hypercycles that share a tangent line passing through the point as their radii tend to infinity is a horocycle.

In the Poincaré disk, hypercycles are represented by arcs of circles that intersect with the boundary circle. If the arc intersects the boundary orthogonally, then the hypercycle is a straight line.
Exotic matter

**Exotic matter** generally refers to forms of matter with a negative real or nonreal complex mass or energy density, but the term is also often used as a broad term that refers to any form of matter that in some sense deviates from "normal" baryonic matter and may have properties that baryonic matter does not have. In this case, exotic matter may also include exotic hadrons that have a different number of quarks or antiquarks from baryons and mesons; degenerate matter; dark matter; exotic atoms and onia; and matter in states that are not the four classical states of matter such as Bose-Einstein condensates.

## Exotic mass

Particles with negative or complex mass exhibit strange properties that may violate the universe's known laws of physics. Applying a force to an object with negative inertial mass will actually cause the object to accelerate towards the force, and objects with negative mass will repel objects with positive and negative mass. Construction of Alcubierre warp drives and wormholes require negative masses. Objects with nonzero imaginary masses will always move faster than the speed of light and move backwards through time. Objects with complex mass may therefore be used to create tachyonic antitelephones, devices that can be used to communicate back in time.

Complexverses are an example of a type of -verse that can allow for forms of exotic matter with negative or complex values for mass.

## References

1. ↑ http://www.daviddarling.info/encyclopedia/E/exotic\_matter.html
Hexadecagram

A **hexadecagram** is a two-dimensional star polygon with sixteen edges, and every fifth vertex connected. It can be considered to be a 16/5-sided polygon. The Bowers acronym for a hexadecagram is **had**.

It has the same number of sides, but a different winding number, as the hexadecagon (1), small hexadecagram (3) and great hexadecagram (7).

## See Also

t
0

{

8
5

}

{\displaystyle t\_0 \{\frac{8}{5} \}}

t
1

{

8
5

}

{\displaystyle t\_1 \{\frac{8}{5} \}}

t

0
,
1

{

8
5

}

{\displaystyle t\_{0,1} \{\frac{8}{5} \}}
Icosihepta-heptacontidi-peton

An **icosihepta-heptacontidi-peton** or **221 polytope** is a uniform polypeton constructed from the E6 group. It is a Gosset polytope.

Its Bowers acronym is **jak**.

## Structure and Sections

### Subfacets

* 27 points (0D)
* 216 line segments (1D)
* 720 triangles (2D)
* 1080 tetrahedra (3D)
* 648 pentachora (4D)
* 72 hexatera (5D)
* 27 pentacrosses (5D)
* 1 icosihepta-heptacontidi-peton (6D)

## References

1. ↑ https://en.wikipedia.org/wiki/2\_21\_polytope
2. ↑ https://bendwavy.org/klitzing/incmats/jak.htm
Holomanga's Unreality Scale

**Holomanga's unreality scale** is one way of sorting verses, by placing them on a scale with less real things (or containers that include less real things) being assigned higher values. Points on the scale are marked on the projective surreal line.

## Reality

Between 0 and 1 represent things that are real, with 0 corresponding to true immediate reality (the Universe) and 1 corresponding to the level of things that are real but arbitarily implausible (contained within the Omniverse). Things between 0 and 1 are said to exist in Reality.

## Paradox Space

Above 1 represent things that are not real, including paradoxes and other impossible things that can't exist within the Omniverse. At around 1 are things that are almost real, save for a single minor contradiction or flaw. At the higher levels, things become less and less real, with greater and even more unresolvable paradoxes. Things greater than 1 are said to exist in Paradox Space.

Structures that contain everything below a certain level of unreality are known as real omniverses. One containing all entities with a reality level below 2 is called the Real Omniverse.

## Unthinkable Reality

At the far end of the scale, at ∞, is things that are infinitely unreal. The Box contains everything less real than this, so on the whole it can be said to have an unreality level of ∞.
Imaginary-order apeirogonal tiling

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

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

## See Also

{
∞
,
2
}

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

{
∞
,
3
}

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

{
∞
,
4
}

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

{
∞
,
5
}

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

{
∞
,
6
}

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

{
∞
,
7
}

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

{
∞
,
8
}

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

{
∞
,
∞
}

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

{
∞
,

π
i

λ

}

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

A **hexacomtelon** is a complex 1-dimensional polytope of 6 points on a complex line. These points have no natural ordering, so no interior can be defined. They can be represented as a hexagon embedded in the complex line.

## References

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

## See Also

{
}

{\displaystyle \{\}}

3

{
}

{\displaystyle \_3\{\}}

4

{
}

{\displaystyle \_4\{\}}

5

{
}

{\displaystyle \_5\{\}}

6

{
}

{\displaystyle \_6\{\}}
Incompatible Being

In -verse theory, an **incompatible being** is a lifeform, whether sapient or nonsapient, that functions on an entirely different set of physical and mathematical laws (compared with the environment or -verse in question), to the point where if it would be introduced into said environment, it would immediately cause a paradox or disruptive event so great that the -verse would be destroyed.

Communication between sets of incompatible beings is possible but no actual information can be transferred in doing so. Generally, the only way to accomplish anything meaningful in terms of communication, without destroying either being's home -verse, is to relay their messages through a third -verse or reality altogether that is safely compatible with both.

It is possible that any lifeforms in any pair of universes could be incompatible. Generally speaking, though, the rate of incompatibility remains low at the multiversal scale, assuming that a multiverse's universes all develop similar characteristics. It increases at the abstract levels of megaverses and archverses, which are less and less related to each other as one ascends.

(To summarize: two beings that cannot interact with each others' environments without completely ruining them are said to be "incompatible".)
Elementary boson

An **elementary boson** is a particle with an integer spin that can not be further decomposed into smaller particles. There are thirteen known types of elementary bosons in the universe, with an additional boson that has not yet been confirmed.

In the Universe, elementary bosons are the force-carrying particles, with elementary fermions being the matter particles.

## Gluons

Gluons are the bosons which carry colour charge and mediate the strong nuclear force.

There are eight types of gluon, corresponding to different colour states. Each gluon carries a combination of colour and anticolour, with the actual colours that a gluon can be being different linear combinations of the colour-anticolour states.

The eight possible colour states of gluons are typically listed as

(
r

b
¯

b

r
¯

)

/

2

{\displaystyle (r\bar{b}+b\bar{r})/\sqrt{2}}

−
i
(
r

b
¯

−
b

r
¯

)

/

2

{\displaystyle -i(r\bar{b}-b\bar{r})/\sqrt{2}}

(
r

g
¯

g

r
¯

)

/

2

{\displaystyle (r\bar{g}+g\bar{r})/\sqrt{2}}

−
i
(
r

g
¯

−
g

r
¯

)

/

2

{\displaystyle -i(r\bar{g}-g\bar{r})/\sqrt{2}}

(
b

g
¯

g

b
¯

)

/

2

{\displaystyle (b\bar{g}+g\bar{b})/\sqrt{2}}

−
i
(
b

g
¯

−
g

b
¯

)

/

2

{\displaystyle -i(b\bar{g}-g\bar{b})/\sqrt{2}}

(
r

r
¯

−
b

b
¯

)

/

2

{\displaystyle (r\bar{r}-b\bar{b})/\sqrt{2}}

(
r

r
¯

b

b
¯

−
2
g

g
¯

)

/

6

.

{\displaystyle (r\bar{r}+b\bar{b}-2g\bar{g})/\sqrt{6}.}

These correspond to the eight Gell-Mann matrices.

Gluons interact with other particles in three different ways:

* A quark of any type may emit or absorb a gluon
* A gluon may emit or absorb a gluon
* Two gluons may interact directly

## W and Z Bosons

W and Z bosons mediate the weak nuclear force.

There are two types of W boson, the W+ and W- bosons, which make a particle-antiparticle pair.

## Photons

Photons mediate the electromagnetic force.

## W and B Bosons

The W and B bosons mediate the electroweak force, the unification of the electromagnetic and the weak nuclear force that only occurs at high energies. There are four of these - three W bosons (the W1, W2 and W3 bosons) and one B boson.

When symmetry breaks between the electromagnetic and weak nuclear force, the B and W3 bosons mix to create the Z boson and the photon, and the W1 and W2 bosons mix to create the W+ and W- bosons.
Infinite-order apeirogonal tiling

An **infinite-order apeirogonal tiling** is a paracompact hyperbolic tiling, in which each point has an infinite number of apeirogons surrounding it.

## See Also

{
∞
,
2
}

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

{
∞
,
3
}

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

{
∞
,
4
}

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

{
∞
,
5
}

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

{
∞
,
6
}

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

{
∞
,
7
}

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

{
∞
,
8
}

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

{
∞
,
∞
}

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

{
∞
,

π
i

λ

}

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

Template:Variant Nav infty infty
Heptorb

A **heptorb** is a 7-dimensional shape made up of the solid interior of a hexasphere. It is the 7-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 =

0

{\displaystyle 0}
* surecton hexavolume =

π

3

60

l

6

{\displaystyle \frac{{\pi}^{3}}{60} {l}^6}
* surzetton heptavolume =

π

3

840

l

7

{\displaystyle \frac{{\pi}^{3}}{840} {l}^7}

### Subfacets

* 1 hexasphere (6D)
* 1 heptorb (7D)
Great faceted hexacosichoron

A **great faceted hexacosichoron**, also known as a **great icosahedral hecatonicosachoron**, is a regular star polychoron composed of 120 great icosahedral cells. It is one of ten Schläfli-Hess polytopes and its dual is the great grand hecatonicosachoron.

Its Bowers acronym is **gofix**.

## See Also

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

A **hyperbolic tube** or **hyperbolic prism** is a shape created from the Cartesian product of a hyperbola and a line segment; in other words, by taking a prism of a hyperbola.

It can also be constructed by taking a pair of infinite rectangles and bending them into branches of a hyperbola.

## Structure and Sections

* 4 hyperbolic branches (1D)
* 2 hyperbolae (1D)
* 2 infinite rectangles (2D)
Great hexadecagram

}}A **great hexadecagram** is a two-dimensional star polygon with sixteen edges and every seventh vertex is connected.

A great hexadecagram has the same symmetry as the hexadecagon, but it has a greater density and winding number than the hexadecagon (1), the small hexadecagram (3), and the hexadecagram (5), at 7.