Pentachoron

Pentachoron
Geometry
Dimensionality	4
Schläfli Symbol	'"`UNIQ--postMath-00000001-QINU`"'
Subfacets
Vertices	5 points
Edges	10 line segments
Faces	10 triangles
Cells	5 tetrahedra
Tera	1 pentachoron
Hypervolumes
Vertex Count	'"`UNIQ--postMath-00000002-QINU`"'
Edges Length	'"`UNIQ--postMath-00000003-QINU`"'
Surface Area	'"`UNIQ--postMath-00000004-QINU`"'
Surcell Volume	'"`UNIQ--postMath-00000005-QINU`"'
Surteron Bulk	'"`UNIQ--postMath-00000006-QINU`"'

A pentachoron is a 4-dimensional simplex. It is also called the pyrochoron under the elemental naming scheme. Its Bowers acronym is "pen".

Properties

Structure

The pentachoron is the pyramid on the tetrahedron, with 4 tetrahedra on each vertex.

Hypervolumes

• vertex count = 5
• edge length = 10
• surface area = $\frac { 5\sqrt { 3 } }{ 2 } { l }^{ 2 }$
• surcell volume = $\frac { \sqrt { 2 } }{ 3 } { l }^{ 3 }$
• surteron bulk = $\frac { \sqrt { 5 } }{ 96 } { l }^{ 4 }$

Subfacets

• 5 points (0D)
• 10 lines (1D)
• 10 triangles (2D)
• 5 tetrahedra (3D)

See also

	Zeroth	First	Second	Third	Fourth	Fifth	Sixth	Seventh	Eighth	Ninth	Tenth
Simplex	Point	Line	Triangle	Tetrahedron	Pentachoron	Hexateron	Heptapeton	Octaexon	Enneazetton	Decayotton	Hendecaxennon
Hypercube	Point	Line	Square	Cube	Tesseract	Penteract	Hexeract	Hepteract	Octeract	Enneract	Dekeract
Cross	Point	Line	Square	Octahedron	Hexadecachoron	Pentarss	Hexarss	Heptarss	Octarss	Ennearss	Decarss
Hypersphere	Point	Line	Circle	Sphere	Glome	Hyperglome	Hexaphere	Heptaphere	Octaphere	Enneaphere	Decaphere