recursal/Fanatic-Fandom huggingface dataset:
Class O star

A **Class O star** is the brightest type of star, sitting on the line between main-sequence and giant. Traditionally, they are colored blue. They are also the rarest type of main-sequence star, making up only 0.00001% of luminous stars.

A typical class O star has a mass of 50 solar masses, a radius of 10 solar radii, a luminosity of 100,000 solar luminosities, a surface temperature of 40000 K and a lifespan of 10 million years.

The habitable zone of a typical O-Class star is on the order of 500 AU. This, coupled with their short lifespans, makes them poor candidates for having solar systems, especially those that support life.

## 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

* Heap, S. R., Lanz, T., and Hubeny, I., *Fundamental Properties of O-Type Stars*
* Mamajek, E., *A Modern Mean Dwarf Stellar Color and Effective Temperature Sequence*. 2019
Definability

**Definability** is a meta-property held by objects that determines how well their properties can be explicitly described. There are three major categories.

If a verse has a certain level of definability, then all of its contents have an equal or lesser level of definability. A verse can not contain something less definable than itself, because the components of a -verse are part of the definition of the verse.

A stronger property than definability is thinkability; things that have a certain level of thinkability are always equally or less definable.

## Definable

Definable objects are those for which the object is theoretically definable in its entirety, such that a complete description of the object could eventually be constructed. Most typical existing -verses with no special contradictions included are thinkable.

On Holomanga's Undefinability Scale, this corresponds to a value of 0.

## Undefinable

Undefinable objects are those to which no properties can be properly ascribed to the whole object, beyond that the object does not, in fact, possess any definite properties across its whole.

On Holomanga's Undefinability Scale, this corresponds to a value of 1.

## Beyond Undefinable

Beyond undefinable objects are those for which giving the property of undefinable would provide more information about their nature. Rather than a distinct category, this represents a state of not being on the map of definability; this averts the paradox of assigning positive properties to objects which are beyond undefinable.

Examples of objects which are beyond undefinable include:

* the Box
* the Omniumverse
Digon

A **digon** is a two-dimensional polygon with two edges. In normal Euclidean space, it is degenerate, enclosing no area, but it can exist as a tiling of the circle.

In Euclidean space, it can be visualized as two line segments with shared endpoints.

## Structure and Sections

### Hypervolumes

* vertex count =

2

{\displaystyle 2}
* edge length =

2
l

{\displaystyle 2 l}
* surface area =

0

{\displaystyle 0}

### Subfacets

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

## See Also

t
0

{
2
}

{\displaystyle t\_0 \{2\}}

t
1

{
2
}

{\displaystyle t\_1 \{2\}}

t

0
,
1

{
2
}

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

t
0

{
1
}

{\displaystyle t\_0 \{1\}}

t
1

{
1
}

{\displaystyle t\_1 \{1\}}

t

0
,
1

{
1
}

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

**Displacement**, also known as **position**, is a vector quantity representing the difference in location between two objects. When these objects are at the vertices of a shape, the displacement between them is the edge length.

It has dimensions of [length].

## Displacement Formulae

v
→

t

r
→

0

{\displaystyle {\vec {v}}t+{\vec {r}}\_{0}}

 Constant acceleration

1
2

a
→

t

2

v
→

0

t

r
→

0

{\displaystyle {\frac {1}{2}}{\vec {a}}t^{2}+{\vec {v}}\_{0}t+{\vec {r}}\_{0}}

 Constant jerk

1
6

ȷ
→

t

3

1
2

a
→

0

t

2

v
→

0

t

r
→

0

{\displaystyle {\frac {1}{6}}{\vec {\jmath }}t^{3}+{\frac {1}{2}}{\vec {a}}\_{0}t^{2}+{\vec {v}}\_{0}t+{\vec {r}}\_{0}}

 Changing absement

A
→

−

A
→

0

t

{\displaystyle {\frac {{\vec {A}}-{\vec {A}}\_{0}}{t}}}

 Changing absity

2

(

B
→

−

B
→

0

−

A
→

0

t

)

t

2

{\displaystyle {\frac {2\left({\vec {B}}-{\vec {B}}\_{0}-{\vec {A}}\_{0}t\right)}{t^{2}}}}
Cardioid

A **cardioid** is an epicycloid produced by rolling a circle outside a fixed circle with the same radius. It loosely resembles a heart, which is where it gets its name.

The cardioid is the simplest example of a heart curve.

## Structure and Sections

### Hypervolumes

* vertex count =

1

{\displaystyle 1}
* edge length =

8
a

{\displaystyle 8a}

### Subfacets

* 1 point (0D)
* 1 cardioid (1D)
Dwarf irregular galaxy

Some of the smallest of all galaxy types, **dwarf irregular galaxies** (dIrr) are very loose and small galaxies containing as few as a couple thousand stars, putting them very close to globular clusters. They are known to have low metallicity, meaning they are good indicators as to what the universe was like when it formed.

While somewhat common as satellites around larger spiral or elliptical galaxies, they are difficult to separate in classification from normal irregular galaxies.

A few dwarf irregular galaxies in our universe include UGC 4459 and the Canis Major Dwarf.
Closed universe

A **closed universe** is a universe which locally has a constant positive curvature everywhere. Closed universes can therefore be in the shape of a hypersphere or elliptic manifold, although the name suggests that the universe is in the shape of any closed manifold (the actual term for any universe in that shape is a compact universe). An example of a -verse on this wiki that can be a closed universe is a pocket universe or nestedverse. The density parameter of a closed universe is greater than 1 and there is enough matter in a closed universe for the gravity of said matter to actually slow down its expansion.

## Life cycle

Closed universes, like most universes, start off their life with a Big Bang. Being typically finite in size, closed universes have a center point in which the rest of the universe expands from. This is typically called a "singularity", or "Protoverse".

Closed universes often expand slower than that of a flat or open universe due to the gravity of the matter affecting the universe's shape.

Eventually, the gravity will completely overcome the expansion of the Universe and it will contract, eventually collapsing in on itself in an event similar to the Big Bang called the Big Crunch. This is unlike in flat and open universes, as they often end their life through Heat death or a Big Rip.

## See Also

* Flat universe - A universe which is locally flat everywhere.
* Open universe - A universe that is locally negatively curved everywhere, and is in the shape of a hyperbolic manifold.

## 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
Core of the Omniverse

The normal depiction of the core

**The Core of the Omniverse** is the singularity in the absolute center of the Omniverse which constantly spews out immeasurable amounts of formless matter and particles mostly in the form of Omnions which turn into various structures and -verses. The Core of the Omniverse is also the first of the Verse Cores.

## **Creation**

During The Divine Ground; the battle between Creator and Destroyer wreaked havoc throughout The Outside, formed the Omniverse. In the center of this formation, time is completely twisted in on itself and mangled due to the strength of the battle between the two supreme beings being almost infinitely high, therefore the instant of the Omniverses creation is being repeated infinitely throughout the lifespan of the Omniverse, therefore, new -verses will never cease to be created.

## **Information**

Civilizations have attempted to take purely formed Omnions in order to gain energy for things such as super-weapons or generally for just storing energy, but getting too close to The Core can often lead to immediate destruction, or even spaghettification like a Black hole. All entering things (if possible) are immediately crushed into 0D space and shot back out in the form of exiting (formless) matter.
Compactverse

A **compactverse** is a universe where all of its spatial dimensions are compact dimensions that function as a boundary to the space inside.

The shape of a compactverse would have to be a closed manifold such as a hypersphere and space would be positively curved. For example, a compact lineverse would be a circle, a compact planeverse would be a sphere, and so on.

Universes that have both linear and compact spatial dimensions can be considered **semi-compactverses** of which tubic universes are an example which take the shape of higher-dimensional analogues of infinitely long tubes (which is the shape of a folded 2D plane).

Compactverses are the loci of all locations from a single point in the higher dimensional space that they sit in, and this point is the point of origin of the -verse, the "center of the universe". The center can never be located on the compactverse, giving any inhabitants the illusion that their universe has no center. Before the expansion into a compactverse, the point is known as a protoverse. Under normal circumstances, compactverses always originate from protoverses.

The most common types of compact dimensions are ones whose dimensions are a Planck length in circumference, the same length as strings that compose larger universes. Any compact dimension at that size or less would be undetectable, so any universe might have a compact dimension curled up at the Planck length without them ever being discovered by anyone. It is likely that the majority of compactverses are a Planck length in size, and they can easily slip inside much larger -verses, compact or not, without causing any harm.

A type of compact dimension that -verses, including compact -verses, may pertain, is a compact temporal dimension. Compact temporal dimensions have cyclic, oscillating time, and timelines would infinitely repeat and never change. Beings that live with compact time exist in an eternal, endless loop, one that they can never escape by themselves. A compactverse that has at least one compact time dimension can be considered a **true compactverse**, a -verse whose spacetime continuum is positively curved.

There is a chance that our universe, is an ever-expanding compactverse, though obviously not one with all of its dimensions curled at the Planck length. The three spatial dimensions that our universe has, may be dimensions of a glome, a 3-dimensional hypersphere, and perhaps, time itself may be a very large compact dimension. The model of the universe that allows the Universe to "be born" and "die" throughout these many timeloops is the **cyclic model** proposed by the **Oscillating Theory**. The latter of the suggestions may never be answered, since no one can live though more than one loop of time, and there is evidence that actually points toward a flat, Euclidean realm-shaped universe, rather than a glome-shaped one, so there is a chance that our universe isn't a compactverse.

## References

1. ↑ https://map.gsfc.nasa.gov/universe/uni\_shape.html
Dark energy

**Dark energy** is a form of energy that acts against gravity and occupies the entirety of the universes in which it exists, uniformly across space. It acts against gravity and accelerates the expansion of them. In the observable universe, it makes up 68.3% of the total mass-energy.

Some types of dark energy with energy density that follows a certain relationship with cosmological scale have specific names. Dark energy that has constant energy density is called the cosmological constant, dark energy that follows a power-law relationship between scale and energy density is called phantom energy, and dark energy that follows an exponential relationship between scale and energy density is called black energy.
Current

**Current** is a physical quantity used in electromagnetism that measures the flow of charges.

In SI units, it is a fundamental quantity with dimensions of [current].

## Conservation of Charge

Current is related to charge through the law of conservation of charge. This relation can be expressed by the continuity equation

# I
−

∂
Q

∂
t

{\displaystyle I = -\frac{\partial Q}{\partial t}}

, where

I

{\displaystyle I}

 is the total current flowing out of a volume and

Q

{\displaystyle Q}

 is the charge enclosed inside that volume. This can also be written in a local form using the current and charge densities as

∇
.

J
→

=
−

∂
ρ

∂
t

{\displaystyle \nabla . \vec J = -\frac{\partial \rho}{\partial t}}

.
Decagram

A **decagram** is 2-Dimensional star polygon with ten vertices, and every third vertex joined. Its Bowers' acronym is **dag**.

## Structure and Sections

### Hypervolumes

* vertex count =

10

{\displaystyle 10}
* edge length =

10
l

{\displaystyle 10l}
* surface area =

5
2

5
−
2

5

l
2

{\displaystyle \frac{5}{2} \sqrt{5 - 2 \sqrt{5} } l^2}

### Subfacets

* 10 points (0D)
* 10 line segments (1D)
* 1 decagram (2D)

## See Also

t
0

{

10
3

}

{\displaystyle t\_0 \{\frac{10}{3} \}}

t
1

{

10
3

}

{\displaystyle t\_1 \{\frac{10}{3} \}}

t

0
,
1

{

10
3

}

{\displaystyle t\_{0,1} \{\frac{10}{3} \}}
Hyperman's Godverse

**Hyperman's Godverse** is the third Godverse within The Barrel. Unlike the Godverses of Creator and Destroyer, there is nothing else within this Godverse except for only Hyperman himself. In fact, this Godverse *is* Hyperman, or at least an extension of himself, in a sense. He is the totality and embodiment of all existence within the -verse, making him completely Omnipresent within it and allowing him to control every aspect of reality and physics in his Godverse, Including things like paradoxes, concepts, Therioes, ideas and philosophies, Metaphysics, Pataphysics, stories, Narratives, mathematics, causalities, realities, unrealities, existences, non-existences, nonexistences, layers, planes, edges, Kingdoms, platonic, Archetypes and Transcendentals, Jungian Archetypes, etc, In this way, Hyperman is technically the embodiment of an entire Omniverse within himself. A being on such a level of existence could, therefore, be capable of grasping the outer limits of the Omniverse.
Carbon star

**Carbon stars**, also known as **Class C stars**, are red giant stars in the asymptotic giant branch that are characterized by atmospheres with an excessive carbon content and very low oxygen content. Any oxygen that would be in a carbon star's atmosphere is bonded to carbon to create carbon monoxide, leaving the rest of the carbon in the star's atmosphere to form other compounds such as CH, CN, C3, and SiC2.

Carbon stars have a temperature range of 1,600 to 5,300 K—comparable in temperature to stars of class L ("deep red"), M ("red"), K ("orange"), or late G ("yellow"). However, due to their atmosphere's high carbon content, carbon stars have very distinct spectra from the aforementioned classes and so are treated as their own class of stars. The carbon in the star's atmosphere also gives carbon stars a sort of "sooty" appearance as well a distinctive colour redder than typical stars of a similar temperature as a considerable amount of blue light is filtered by the atmosphere.

Class C is divided into subclasses according to their spectra.

* Classical carbon stars: Originally were known as **Class R** and **Class N** stars. Abundance of carbon is likely a product of helium fusion.
	+ C-R: No enhanced barium line, atmosphere absorbs less blue light compared to C-N stars
	+ C-N: Blue light is almost completely absorbed, weak isotopic bands
* Non-classical carbon stars:
	+ C-J: Very strong bands of C2 and CN
	+ C-H: Very strong CH absorption. Likely formed after the evolution of a main sequence star to a red giant after it has accreted carbon-rich material from a companion classical carbon star.
	+ C-Hd: Hydrogen-deficient. Weak or absent bands of hydrogen and/or CH.

## References

* Various; Carbon star - Wikipedia, the free encyclopedia

## See Also

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

A **0-Dimensional Space** is a space in which every position can be described in a point. In other words, there is only one possible position in zero dimensional space, so no information is required to describe the location.

strictly,a zero dimensional space will have no time or space so it will be in a fixed and single state, though sometimes spaces with some time dimensions (such as 0+1 dimensional space) are considered to be zero-dimensional.

A verse that is zero dimensional is called a Pointverse.
Deadzone

A **Deadzone** is a type of Superweapon discovered by The Eternal Imperium and created by taking a fragment of the Core of the Omniverse and using incredibly advanced technology to essentially cannibalize the fragment. Being some of the most stable regions in the Omniverse, no new energy of any form can be created within a Deadzone, thus meaning whatever is trapped inside it cannot move or affect anything in any way, leaving them eternally trapped until the controller of the Deadzone chooses to release them. *if* the controller of the Deadzone chooses to release them.

The Eternal Imperium mass-produced an infinite number of Deadzones when the technology was first discovered and due to their frightening capabilities, The Mevalkagna destroyed almost all Deadzones during their purge of advanced technology. However, a few survived, and fell into the hands of the Eternal Legion. No entity, group, organization or civilization has since been able to create Deadzones, with the exception of the A.I. Terminus.

## **Creation**

The Core of the Omniverse holds within it an exact copy of the Omniverse as it was when it was first created and unlike the rest of the Omniverse, never changes, constantly birthing itself over and over, creating whole Omniverses worth of matter and energy constantly, thus accounting the Omniverse's incredible size. The Eternal Imperium were able to find a way to invert this using their advanced technology, and instead of containing a constant instant of supreme creation, a Deadzone contains a constant instant of energy exhaustion. Similar to the heat death of the Universe, within a Deadzone all forms of Omniversal existence lose power and with it, form, resulting in a form of existence where everything is static. Nothing has ceased to exist, but without movement and progress, with or without time, existence as we know it cannot happen, as nothing will ever change. When isolated into a single small fraction of reality in the form of a Deadzone, it becomes a frighteningly powerful weapon. Anything trapped within a Deadzone will remain exactly as it was when it entered, completely unable to do or change anything, as no new energy can be created.
Apeirogon

An **Apeirogon** is a 2-dimensional polygon with a countably infinite number of edges. It can be visualized as a tiling of a one-dimensional line by line segments. In the hyperbolic plane, regular apeirogons are circumscribed by a horocycle, and their lines of symmetry converge to a point at infinity. More general apeirogons include the apeirograms (

{

∞
n

}

{\displaystyle \{\frac{\infty}{n}\}}

 for natural

n

{\displaystyle n}

), failed star polygons (

{
x
}

{\displaystyle \{x\}}

 for irrational real

x

{\displaystyle x}

), and pseudogons (

{
z
}

{\displaystyle \{z\}}

 for nonzero imaginary

z

{\displaystyle z}

).

Its Bowers acronym is **aze**.

## Structure and Sections

### Hypervolumes

* vertex count =

ℵ
0

{\displaystyle \aleph\_0}
* edge length =

∞
l

{\displaystyle \infty l}
* surface area =

∞

l

2

{\displaystyle \infty {l}^{2}}

### Sub-facets

* ℵ0 points (0D)
* ℵ0 line segments (1D)
* 1 apeirogon (2D)

## See Also

* Polytope Wiki. "Apeirogon"

t
0

{
∞
}

{\displaystyle t\_0 \{\infty\}}

t
1

{
∞
}

{\displaystyle t\_1 \{\infty\}}

t

0
,
1

{
∞
}

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

A hendekeract is the 12-dimensional hypercube. It can be considered to be a prism with a hendekeract as the base.

Under the elemental naming scheme, it is called a **geohendon**.

## Structure and Sections

### Subfacets

* 4096 points (0D)
* 24576 line segments (1D)
* 67584 squares (2D)
* 112640 cubes (3D)
* 126720 tesseracts (4D)
* 101376 penteracts (5D)
* 59136 hexeracts (6D)
* 25344 hepteracts (7D)
* 7920 octeracts (8D)
* 1760 enneracts (9D)
* 264 dekeracts (10D)
* 24 hendekeracts (11D)
* 1 hendekdekeract (12D)

### Hypervolumes

* vertex count =

4096

{\displaystyle 4096}
* edge length =

24576
l

{\displaystyle 24576l}
* surface area =

67584

l

2

{\displaystyle 67584l^{2}}
* surcell volume =

112640

l

3

{\displaystyle 112640l^{3}}
* surteron bulk =

126760

l

4

{\displaystyle 126760l^{4}}
* surpeton pentavolume =

101376

l

5

{\displaystyle 101376l^{5}}
* surecton hexavolume =

59136

l

6

{\displaystyle 59136l^{6}}
* surzetton heptavolume =

25344

l

7

{\displaystyle 25344l^{7}}
* suryotton octavolume =

7920

l

8

{\displaystyle 7920l^{8}}
* surxennon enneavolume =

1760

l

9

{\displaystyle 1760l^{9}}
* surdakon dekavolume =

264

l

10

{\displaystyle 264l^{10}}
* surhendon hendekavolume =

24

l

11

{\displaystyle 24l^{11}}
* surdakon dodekavolume =

l

12

{\displaystyle l^{12}}
Acceleration

**Acceleration** is a vector quantity representing the change in velocity of an object over time. The acceleration of an object is the result to net forces acting upon said object, and is inversely proportional to the mass of the object.

It has dimensions of [length][time]-2.

## Acceleration Formulae

ȷ
→

t

a
→

0

{\displaystyle \vec \jmath t + \vec a\_0}
Digonal dihedron

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

{
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

{
2
,
2
}

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

t
1

{
2
,
2
}

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

t
2

{
2
,
2
}

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

t

0
,
1

{
2
,
2
}

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

t

1
,
2

{
2
,
2
}

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

t

0
,
2

{
2
,
2
}

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

t

0
,
1
,
2

{
2
,
2
}

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

{
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\}}
Edge

**Edges** are the one-dimensional constituents of a polytope, one-dimensional subfacets. The edges of a polygon are the boundary of said polygon. Edges of a polytope are formed when two or more facets meet each other. Exotic polytopes can be created if more than two faces are joined together to create an edge.

Edges are the facets of a polygon, the ridges of a polyhedron, and the peaks of a polychoron.

## See Also

...Spire · Peak · Ridge · Facet · Polytope
2002 MS4

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 → **2002 MS4**

## Climate

### Temperature

-230.15°C

**2002 MS4** is a dwarf planet orbiting the Sun in the Kuiper Belt of our Solar System and currently the largest object in the Solar System without a name. With a radius of 393.5 km, 2002 MS4 is the eighth largest Trans-Neptunian object in terms of diameter, comparable in size to Ceres and Orcus.
Dimension

A **dimension** is a degree of freedom in which position can vary. Each degree of freedom can be indexed by a single variable, which means that the dimensionality of a space is the number of coordinates needed to specify a point in that space. For example, a solid cube requires an x, y and z coordinate to define a position within, so it is three-dimensional.

In many physical theories, dimensions can either be spatial, temporal, or compact. Spatial dimensions are typical dimensions, allowing for free movement in all directions. Temporal dimensions correspond to time, and only allow changes to propagate in one direction. Compact dimensions are small, finite and periodic, meaning that they do not have a clear extent macroscopically but alter the behavior of microscopic phenomena.

In mathematics, other notions of the word "dimension" can be considered and serve as useful for studying more complicated objects such as fractals. One of these notions is **Hausdorff dimensionality**. The Hausdorff dimension of a metric space

X

{\displaystyle X}

 is the infimum of the set of all

d
∈
[
0
,
∞
)

{\displaystyle d\in [0,\infty )}

 such that the

d

{\displaystyle d}

-dimensional Hausdorff measure of

X

{\displaystyle X}

 is 0.
Cone

Cone with conic sections

A **cone** is a three-dimensional shape produced by creating a pyramid with a disc as the base. It is also the segmentotope between a disc and a point.

## Structure and Sections

A right circular cone is composed of one disc as a base with all points on the circle joined to a point a set distance from the center. The surface created from the process is known as a nappe segment.

A 1-dimensional shape that creates a boundary of a planar intersection within the cone is called a **conic section**, or simply **conic**. The non-degenerate conics are the ellipse, the parabola, and the hyperbola, with the circle usually considered one in its own right.

### Hypervolumes

* vertex count =

1

{\displaystyle 1}
* edge length =

π
l

{\displaystyle \pi l}
* surface area =

π

π
2

4

l
2

π

l
2

s

{\displaystyle \pi \frac {\pi^2}{4} l^2 + \pi \frac {l}{2} s}
* surcell volume =

π
12

l
2

h
2

{\displaystyle \frac {\pi}{12} l^2 h^2}

### Subfacets

* 1 point (0D)
* 1 circle (1D)
* 1 disc (2D)
* 1 nappe segment (2D)
* 1 cone
Infinite-order octagonal tiling

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

## 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\}}
Communality

**Communality** is a category of sentience corresponding to a processing rate of 1022 bits/sec (a sentience quotient of 20-30 for a 100 kg individual). A communal sentient uses cultural information storage in order to process information, and has a consciousness based upon an innate sociocultural awareness.

Communally sentient individuals have physical and social generalisation; each individual could take up any social role.

They also have a new level of awareness above the old, giving them a full awareness of their society, which allows them to innately sense what is good for society.

## References

* http://www.xenology.info/Xeno/25.2.2.htm
Infinite-order pseudogonal tiling

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

An **infinite-order pseudogonal tiling** is a regular hyperbolic tiling constructed by joining an infinite amount of pseudogons of the same symmetry to a vertex.

## 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\}}

{

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}\}}
1 42 polytope

The **142 polytope**, also known as the **diacositetracont-dischiliahectohexaconta-zetton**, is a polyzetton based around the bifurcating Coxeter-Dynkin diagram with sequences of length 1, 4 and 2, with a single ringed node at the end of the sequence of length 1.

It has the Bowers acronym **bif** and the Bowers symbol o3o3o3x \*c3o3o3o3o.

## Structure and Sections

### Subfacets

* 17280 points (0D)
* 483840 line segments (1D)
* 2419200 triangles (2D)
* 3628800 tetrahedra (3D)
* 1693440 pentachora (4D)
* 604800 hexadecachora (4D)
* 241920 demipenteracts (5D)
* 483840 hexatera (5D)
* 6720 pentacontatetrapeta (6D)
* 30420 demihexeracts (6D)
* 69120 heptapeta (6D)
* 240 132 polytopes (7D)
* 2160 demihepteracts (7D)
* 1 142 polytope (8D)
Absement

**Absement**, also known as **absition**, is a vector quantity that measures the sustained displacement of an object from it's initial position.

It has dimensions of [length][time].

## Absement Formulae

A
→

=

∫

t
0

t

r
→

d
t

{\displaystyle \vec A = \int\_{t\_0}^t \vec r ~ \text{d}t}

 Constant position

r
→

t

A
→

0

{\displaystyle \vec rt + \vec A\_0}
Cyclosphere

A **cyclosphere** is a five-dimensional rotatope constructed from the product of a ball and a disc. This means that it can be considered to be a duoprism with a ball and disc as factors. It is composed of two curved 4-D cells joined by a 3-D surface.

## Structure and Sections

The cyclosphere's sections come in two types. Either there is a disc expanding to a duocylinder and back, or a ball expanding to a spherinder and back.
Digonal prism

A **digonal prism** is a three-dimensional prism with a digon as the base. In normal Euclidean space, it is degenerate, but it can exist as a tiling of the sphere.

It can also be considered to be a truncated, bitruncated or cantellated digonal dihedron.

## See Also

t
0

{
2
,
2
}

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

t
1

{
2
,
2
}

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

t
2

{
2
,
2
}

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

t

0
,
1

{
2
,
2
}

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

t

1
,
2

{
2
,
2
}

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

t

0
,
2

{
2
,
2
}

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

t

0
,
1
,
2

{
2
,
2
}

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

t

0
,
1

{
2
,
2
}

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

t

0
,
1

{
2
,
3
}

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

t

0
,
1

{
2
,
4
}

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

t

0
,
1

{
2
,
5
}

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

t

0
,
1

{
2
,
6
}

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

t

0
,
1

{
2
,
7
}

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

t

0
,
1

{
2
,
8
}

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

t

0
,
1

{
2
,
∞
}

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

t

0
,
1

{
2
,

π
i

λ

}

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

A **cubic torus** is a 4-dimensional shape constructed from the cartesian product of a circle and a cube. It can also be considered as a prism with a square torus as the base, or as a shape constructed from a tesseract with the ends connected in a ring.

## Structure and Sections

### Subfacets

* 8 circles (1D)
* 12 tubes (2D)
* 6 square tori (3D)
* 1 cubic torus (4D)
Heaven

In Abrahamic religions, **Heaven** is the place destined for all those that are truly loyal to God, or Allah (Arabic for God). This is in very stark contrast to Hell.

There is also the view that heaven can just be the state of mind of pure happiness felt by good spirits living in the Spirit World that have a tranquil conscience and are collecting the rewards of their correct actions. In that sense, it would be just a type of Internal Reality.
Deltahedron

A convex **deltahedron** (not to be confused with a deltohedron)is a class of special cases of isohedral polytopes that consist of all convex polyhedra with equilateral triangular faces. They can be generalized to convex polytopes with simplices as subfacets. There are only eight convex deltahedra.

They are the

* Tetrahedron
* Triangular bipyramid
* Octahedron
* Pentagonal bipyramid
* Snub disphenoid
* Triaugmented triangular prism
* Gyroelongated square bipyramid
* Icosahedron
Ignotum

**Ignotum** is an "entity" which resides in Metempiric Space, and has the ability to manipulate entire Altarcae.

## **Information**

Not much can be said about a being that lives in a space that holds no properties, since being in Metempiric Space would require one to hold not many properties themselves. Such goes for Ignotum.

Ignotum is an amalgamation of an infinite number of powerful entities between different altarcae merging through unnatural means and gaining self awareness.

Ignotum's power is the equivalent of that of a top tier Aspect Lord.
Ball

A **ball** is a 3-dimensional shape made up of the solid interior of a sphere.

The symmetry group of a ball is O(3), because all rotations and reflections about the center of the ball leave the ball unchanged.

## Structure and Sections

The ball is made up of a single curved face. Its sections look like a point growing to a disc before shrinking again.

### Hypervolumes

* vertex count =

0

{\displaystyle 0}
* edge length =

0

{\displaystyle 0}
* surface area =

π

l
2

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

1
6

π

l
3

{\displaystyle \frac{1}{6}\pi l^3}

### Subfacets

* 1 sphere (2D)
* 1 ball (3D)

### Equations

The surface of a ball of radius r, centered at the origin, can be given by

x
2

y
2

z
2

=

r
2

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

.

### Notations

* Toratopic notation:

(

)

{\displaystyle (|)}
* Tapertopic notation:

3

{\displaystyle 3}

## Coordinate System

The coordinate system corresponding to the ball is called spherical polar coordinates, with the three coordinates being

(

r
,
θ
,
ϕ

)

{\displaystyle \left( r, \theta, \phi \right)}

.

These can be converted to Cartesian coordinates using the formulae

x

=
r

sin
⁡
θ

cos
⁡
ϕ

y

=
r

sin
⁡
θ

sin
⁡
ϕ

z

=
r

cos
⁡
θ

{\displaystyle \begin{align}
x &= r \, \sin\theta \, \cos\phi \\
y &= r \, \sin\theta \, \sin\phi \\
z &= r \, \cos\theta
\end{align}}

The position vector is hence given by

r
→

=

(

r
sin
⁡
θ
cos
⁡
ϕ

r
sin
⁡
θ
sin
⁡
ϕ

r
cos
⁡
θ

)

{\displaystyle \vec{r} = \begin{pmatrix}
r \sin\theta \cos\phi \\
r \sin\theta \sin\phi \\
r \cos\theta \\
\end{pmatrix}}

.This means the three unit vectors are

r
^

=

(

sin
⁡
θ
cos
⁡
ϕ

sin
⁡
θ
sin
⁡
ϕ

cos
⁡
θ

)

{\displaystyle \hat r = \begin{pmatrix}
\sin\theta \cos\phi \\
\sin\theta \sin\phi \\
\cos\theta \\
\end{pmatrix}}

,

θ
^

=

(

cos
⁡
θ
cos
⁡
ϕ

cos
⁡
θ
sin
⁡
ϕ

−
sin
⁡
θ

)

{\displaystyle \hat \theta = \begin{pmatrix}
\cos\theta \cos\phi \\
\cos\theta \sin\phi \\
-\sin\theta \\
\end{pmatrix}}

 and

ϕ
^

=

(

−
sin
⁡
ϕ

cos
⁡
ϕ

0

)

{\displaystyle \hat \phi = \begin{pmatrix}
-\sin\phi \\
\cos\phi \\
0 \\
\end{pmatrix}}

.

## Generalizations

Generalization of ball for euclidean spaces of arbitrary dimension is hyperball (n-ball).

Speaking even more generally, for a metric space (*M*,*d*), where *M* is a set and *d* is a metric (distance function), the open ball

B
o

{\displaystyle B\_o}

 of radius *r* and center *c* is the set:

B
o

=
{
x
∈
M

d
(
x
,
c
)
<
r
}

{\displaystyle B\_o=\{x\in M|d(x,c)<r\}}

and the closed ball

B
c

{\displaystyle B\_c}

 of radius r and center c is the set:

B
c

=
{
x
∈
M

d
(
x
,
c
)
≤
r
}

{\displaystyle B\_c=\{x\in M|d(x,c)\le r\}}

.

## See Also

S

2

{\displaystyle \mathbb S^{2}}

T

2

{\displaystyle \mathbb{T}^2}

2

T

2

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

3

T

2

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

4

T

2

{\displaystyle 4\mathbb{T}^2}
Hypermatter drive

A **hypermatter drive** is a technique for communication and travel between different universes. They operate by producing, maintaining and manipulating hypermatter in order to send signals that escape their local universe and influence nearby universes.

The amplitude of these signals is often very small and they attenuate rapidly, so hypermatter drives are ineffective for long distance communication. This is compounded if complicated messages need to be sent; the signals from hypermatter drives are typically simple, often just encoding single bits of information.

Hypermatter drive technology is typically supplanted by infomatter drive technology when a receiver is constructed in the target universe. These usually represent cooperation between two universal civilisations, though it is possible to assemble a reciever using only hypermatter with great difficulty.
Conglomerateverse

A **conglomerateverse** is a verse that is made up of a proper conglomerate of particles, rather than a set of particles like in an ordinary verse or a proper class of particles like in a classverse. Each conglomerateverse contains multiple classverses.

One way of considering the size of a conglomerate is that for each set of ordinal numbers, there is a corresponding particle.

## See also

* Classverse
* Secondclassverse
* Absoluteverse
Atom

Observation of a hydrogen atom's wavefunction

An **atom** is the smallest component of ordinary matter that has the properties of a chemical element. They are overall neutral, with a heavy, positively charged nucleus made up of protons and neutrons surrounded by a bound cloud of electrons. They can bond to other atoms to form molecules.

## Structure

### Nucleus

The nucleus is situated in the center of the atom. It is made up out of nucleons, the two types of which are the positively charged protons which determine the chemical element and the neutral neutrons which determine the isotope.

### Electrons

Electrons are small elementary particles which surround the nucleus in orbitals, the shape of which correspond to eigenfunctions of the Schrödinger equation for the atom. Orbitals can be described by four quantum numbers: the principal quantum number n associated with the total energy, the azimuthal quantum number ℓ associated with the orbital angular momentum squared, the magnetic quantum number mℓ associated with one component of the orbital angular momentum and the spin quantum number ms associated with the electronic spin.

For a given value of n (called the shell), the value of ℓ (called the subshell) can range between 0 and n-1, and the value of m (called the orbital) can range between -ℓ and ℓ. There are two possible values for ms.
Asteroid

*This article is about class of minor planet. Not to be confused with Astroid.*

951 Gaspra, an asteroid that orbits close to the inner edge of the Asteroid belt.

## Scale

### Mass

Variable

An **asteroid** is a minor planet generally not in hydrostatic equilibrium orbiting some type of stellar mass and has not cleared its neighboring region. Typically, they orbit a star in a Solar System within large belt that consists of other minor planets, as their gravity is not strong enough to clear its neighbourhood. The belt consisting of asteroids in our solar system is the **Main Belt**, generally known as the asteroid belt.

Larger asteroids are called **planetoids** and smaller ones are called **meteoroids**. Asteroids can also be classed by what their main composition is. Carbonaceous asteroids are **C-type asteroids**, metallic asteroids are **M-type asteroids**, and silicaceous asteroids are **S-type asteroids**.
Bitruncated pentachoron

A **bitruncated pentachoron**, or **decachoron** is a uniform polychoron created from bitruncating a pentachoron. It is composed of 10 truncated tetrahedral cells.

Its Bowers acronym is **deca**.

## Structure and Sections

### Subfacets

* 30 points (0D)
* 60 line segments (1D)
* 20 triangles (2D)
* 20 hexagons (2D)
* 10 truncated tetrahedra (3D)
* 1 bitruncated pentachoron (4D)

## See Also

* Polytope Wiki. "Decachoron".
* Bowers, Jonathan. "Category 7: Bitruncates".

t
0

{
3
,
3
,
3
}

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

t
1

{
3
,
3
,
3
}

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

t
2

{
3
,
3
,
3
}

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

t
3

{
3
,
3
,
3
}

{\displaystyle t\_3 \{3,3,3\}}

t

0
,
1

{
3
,
3
,
3
}

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

t

1
,
2

{
3
,
3
,
3
}

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

t

2
,
3

{
3
,
3
,
3
}

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

t

0
,
2

{
3
,
3
,
3
}

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

t

1
,
3

{
3
,
3
,
3
}

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

t

0
,
1
,
2

{
3
,
3
,
3
}

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

t

1
,
2
,
3

{
3
,
3
,
3
}

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

t

0
,
3

{
3
,
3
,
3
}

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

t

0
,
2
,
3

{
3
,
3
,
3
}

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

t

0
,
1
,
3

{
3
,
3
,
3
}

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

t

0
,
1
,
2
,
3

{
3
,
3
,
3
}

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

**Arhadalite** is a red-colored (when seen through normal human eyes) mineral that occurs naturally in some archverses. It possesses a set of unusual properties, including a structural similarity to both stringshard and metamesonium at the quantum level.

Like stringshard or metamesonium, it interacts with time differently than other materials. Arhadalite exists at every point along not just a timeline, but a timecube; it occupies three dimensions of time and can interact with other materials in the past, present, or future along three axes. Any given piece of arhadalite is infinitely old and has an infinite lifespan remaining.

This leads to a somewhat lesser-known property. There is no process that actually *creates* arhadalite, and although an infinite amount exists throughout the infinite omniverse, as new -verses form with arhadalite reserves within them, deposits of the mineral elsewhere in the omniverse vanish as they are "reallocated". Similarly, no process, reaction, or event can destroy arhadalite, as any lost quantity appears somewhere else.

Entities such as the Hexagon Lords and The Overseer have used arhadalite weapons in their trans-temporal combat, and civilizations like the Guardians of Aleph regularly mass-produce these for their much larger-scale wars.
Dodecadodecahedron

A **dodecadodecahedron** is a uniform polyhedron that can be constructed from rectifying a great dodecahedron or small stellated dodecahedron. In Euclidean space, it is self-intersecting and has 12 pentagonal and 12 pentagrammic faces.

Its dual is the medial rhombic triacontahedron.

Its Bowers acronym is **did**.

## Structure and Sections

### Subfacets

* 30 points (0D)
* 60 line segments (1D)
* 12 pentagons (2D)
* 12 pentagrams (2D)
* 1 dodecadodecahedron (3D)

## See Also

* Polytope Wiki. "Dodecadodecahedron".
* Bowers, Jonathan. "Polytope Category 3: Quasiregulars".
Dekasphere

A **dekasphere** is a 10-dimensional surface produced by finding the set of all points that are an equal distance from another point in 11-dimensional space. Because it is curved, it is often represented embedded in 11-dimensional space. A dekasphere is the shape of the exterior of an hendekorb. It is the 10-dimensional hypersphere.
Bright giant

A **bright giant** is a star intermediate between a giant star and a supergiant in luminosity and spectrum. They span the entire spectral classification; red bright giants tend to be large, like normal red giants, while blue bright giants are often smaller, though still several times the radius of the Sun. On an H-R diagram, bright giants are visible just above the giant branch.

Bright giants evolve to supergiants if they are massive enough, or progress to later stages of stellar evolution like the asymptotic giant branch otherwise.

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

A hexagonal pyramid is a three-dimensional polytope created by taking the pyramid of a hexagon, which means that it also the segmentotope between a hexagon and a point. Its Bowers' acronym is **hippy**.

The regular form of a hexagonal pyramid, where all edges are the same length and all faces are regular, is flat. This is because the height of a regular n-gonal pyramid is given by the formula

1
−

1
4

csc
2

⁡

(

π
n

)

{\displaystyle \sqrt{1 - \frac{1}{4} \csc^2 \left( \frac{\pi}{n} \right) }}

, which is equal to zero when n=6.

## See Also

(
)
∧
{
3
}

{\displaystyle () \wedge \{3\}}

(
)
∧
{
4
}

{\displaystyle () \wedge \{4\}}

(
)
∧
{
5
}

{\displaystyle () \wedge \{5\}}

(
)
∧
{
6
}

{\displaystyle () \wedge \{6\}}
Hilbert space

A **Hilbert space** is an real or complex vector space equipped with an inner product (such as the dot product) that is complete with respect to the distance function defined by the inner product

d
(
z
,
w
# )

⟨
z
−
w
,
z
−
w
⟩

{\displaystyle d(z,w) = \sqrt{\langle z-w, z-w \rangle}}

. The inner product

⟨
z
,
w
⟩

{\displaystyle \langle z, w \rangle}

 for all complex arguments has to satisfy the following three properties in order for the space to be a Hilbert space:

* ⟨
z
,
w
# ⟩

⟨
w
,
z
⟩

∗

{\displaystyle \langle z, w \rangle = {\langle w, z \rangle}^\*}

 where

∗

{\displaystyle {}^\*}

 is the complex conjugate
* ⟨
z

x
1

w

x
2

,
y
# ⟩
z
⟨

x
1

,
y
⟩
w
⟨

x
2

,
y
⟩

{\displaystyle \langle zx\_1 + wx\_2, y\rangle = z\langle x\_1, y\rangle + w\langle x\_2, y\rangle}
* 0
≤
⟨
z
,
z
⟩

{\displaystyle 0 \leq \langle z, z \rangle}

Hilbert spaces can have a finite or infinite cardinal number of dimensions. Examples of finite-dimensional Hilbert spaces include Euclidean spaces, complex vector spaces, and Lebesgue spaces with other non-Euclidean metrics such as taxicab or Chebyshev. An example of an infinite dimensional Hilbert space is **L2**, the set of all square-integrable functions, complex-valued functions on the real numbers f such that f2 has a finite integral over the real line.

Hilbert spaces are always Banach spaces, as they are complete and a norm can be defined.

Hilbert spaces have many applications throughout many branches of mathematics and physics such as Fourier analysis, quantum mechanics, and ergodic theory.
Exaverse

The **Exaverse** is the seventh nested level of the metric -verse series and the fourth lowest-level archverse. This -verse contains a finite or infinite

amount of petaverses, which are the sixth nested level. It is contained by the Zettaverse, which is an finite or infinite set of exaverses.

Unlike Petaverses the high density regions are on the outside of the center. The center of a Exaverse is one of the lowest density regions of any Archverse.
Half-plane

A **half-plane** is an infinite two-dimensional shape comprising half of a Euclidean plane, with a Euclidean line as its boundary. Such a half-plane divides the Euclidean plane into two sides, an inside and an outside.

It can be constructed by subtracting a Euclidean line from the plane, and then taking one of the two spaces produced and using the line as its boundary.