Penteract

Penteract
A 5-D equivalent to the Rubik's Cube, a 3x3x3x3x3.
Dimensionality	5
Schläfli Symbol	'"`UNIQ--postMath-00000001-QINU`"'
Symmetry	Full penteractic symmetry
Bowers acronym	pent
Subfacets
Vertices	32 points
Edges	80 line segments
Faces	80 squares
Cells	40 cubes
Tera	10 tesseracts
Peta	1 penteract
Hypervolumes
Vertex Count	'"`UNIQ--postMath-00000002-QINU`"'
Edge Length	'"`UNIQ--postMath-00000003-QINU`"'
Surface Area	'"`UNIQ--postMath-00000004-QINU`"'
Surcell Volume	'"`UNIQ--postMath-00000005-QINU`"'
Surteron Bulk	'"`UNIQ--postMath-00000006-QINU`"'
Surpeton Pentavolume	'"`UNIQ--postMath-00000007-QINU`"'

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

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

Structure and Sections

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

Hypervolumes

• vertex count =$32$
• edge length =$80l$
• surface area =$80{ l }^{ 2 }$
• surcell volume =$40{ l }^{ 3 }$
• surteron bulk =$10{ l }^{ 4 }$
• surpeton pentavolume =${ l }^{ 5 }$

Subfacets

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

Gallery

See Also

Dimensionality	Negative One	Zero	One	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	Eleven	Twelve	Thirteen	Fourteen	Fifteen	Sixteen	...	Aleph null
Simplex $\{3^{n-1}\}$	Null polytope $)($ $\emptyset$	Point $()$ $\mathbb{B}^0$	Line segment $\{\}$ $\mathbb{B}^1$	Triangle $\{3\}$	Tetrahedron $\{3^2\}$	Pentachoron $\{3^3\}$	Hexateron $\{3^4\}$	Heptapeton $\{3^5\}$	Octaexon $\{3^6\}$	Enneazetton $\{3^7\}$	Decayotton $\{3^8\}$	Hendecaxennon $\{3^9\}$	Dodecadakon $\{3^{10}\}$	Tridecahendon $\{3^{11}\}$	Tetradecadokon $\{3^{12}\}$	Pentadecatradakon $\{3^{13}\}$	Hexadecatedakon $\{3^{14}\}$	Heptadecapedakon $\{3^{15}\}$	...	Omegasimplex
Cross $\{3^{n-2},4\}$				Square $\{4\}$	Octahedron $\{3, 4\}$	Hexadecachoron $\{3^2, 4\}$	Pentacross $\{3^3, 4\}$	Hexacross $\{3^4, 4\}$	Heptacross $\{3^5, 4\}$	Octacross $\{3^6, 4\}$	Enneacross $\{3^7, 4\}$	Dekacross $\{3^8, 4\}$	Hendekacross $\{3^9, 4\}$	Dodekacross $\{3^{10}, 4\}$	Tridekacross $\{3^{11}, 4\}$	Tetradekacross $\{3^{12}, 4\}$	Pentadekacross $\{3^{13}, 4\}$	Hexadekacross $\{3^{14}, 4\}$	...	Omegacross
Hydrotopes $\{3^{n-2}, 5\}$				Pentagon $\{5\}$	Icosahedron $\{3, 5\}$	Hexacosichoron $\{3^2, 5\}$	Order-5 pentachoric tetracomb $\{3^3, 5\}$	Order-5 hexateric pentacomb $\{3^4, 5\}$	...
Hypercube $\{4, 3^{n-2}\}$				Square $\{4\}$	Cube $\{4,3\}$	Tesseract $\{4, 3^2\}$	Penteract $\{4, 3^3\}$	Hexeract $\{4, 3^4\}$	Hepteract $\{4, 3^5\}$	Octeract $\{4, 3^6\}$	Enneract $\{4, 3^7\}$	Dekeract $\{4, 3^8\}$	Hendekeract $\{4, 3^9\}$	Dodekeract $\{4, 3^{10}\}$	Tridekeract $\{4, 3^{11}\}$	Tetradekeract $\{4, 3^{12}\}$	Pentadekeract $\{4, 3^{13}\}$	Hexadekeract $\{4, 3^{14}\}$	...	Omegeract
Cosmotopes $\{5, 3^{n-2}\}$				Pentagon $\{5\}$	Dodecahedron $\{5, 3\}$	Hecatonicosachoron $\{5, 3^2\}$	Order-3 hecatonicosachoric tetracomb $\{5, 3^3\}$	Order-3-3 hecatonicosachoric pentacomb $\{5, 3^4\}$	...
Hyperball $\mathbb B^n$				Disk $\mathbb B^2$	Ball $\mathbb B^3$	Gongol $\mathbb B^4$	Pentorb $\mathbb B^5$	Hexorb $\mathbb B^6$	Heptorb $\mathbb B^7$	Octorb $\mathbb B^8$	Enneorb $\mathbb B^9$	Dekorb $\mathbb B^{10}$	Hendekorb $\mathbb B^{11}$	Dodekorb $\mathbb B^{12}$	Tridekorb $\mathbb B^{13}$	Tetradekorb $\mathbb B^{14}$	Pentadekorb $\mathbb B^{15}$	Hexadekorb $\mathbb B^{16}$	...	Omegaball $\mathbb B^{\aleph_0}$

$\{2,3,3,3\}$	$\{3,3,3,3\}$	$\{4,3,3,3\}$	$\{5, 3, 3, 3\}$
Pentachoric hosoteron	Hexateron	Penteract	Order-3 hecatonicosachoric tetracomb

$\{4,3,3,2\}$	$\{4,3,3,3\}$	$\{4,3,3,4\}$	$\{4,3,3,5\}$
Tesseractic diteron	Penteract	Tesseractic tetracomb	Order-5 tesseractic tetracomb

Template:Variant Nav 4 3 3 3