Hexadecachoric pyramid

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Hexadecachoric pyramid
File:Hexadecachoric pyramid.png
Rank4
TypeSegmentotope
Notation
Bowers style acronymHexpy
Coxeter diagramoo4oo3oo3ox&#x
Elements
Tera16 pentachora, 1 hexadecachoron
Cells16+32 tetrahedra
Faces24+32 triangles
Edges8+24
Vertices1+8
Vertex figures1 hexadecachoron, edge length 1
 8 octahedral pyramids, edge length 1
Measures (edge length 1)
Circumradius
Hypervolume
HeightPoint atop hex:
Central density1
Related polytopes
DualTesseractic pyramid
ConjugateNone
Abstract & topological properties
Flag count2304
Euler characteristic0
OrientableYes
Properties
SymmetryB4×I, order 384
ConvexYes
NatureTame

The hexadecachoric pyramid is a Blind polytope and CRF segmentoteron. It has 8 regular pentachora and 1 regular hexadecachoron as facets. It is a pyramid based on the hexadecachoron.

It is part of an infinite family of Blind polytopes known as the orthoplecial pyramids. It is one of two non-uniform Blind polytopes in five dimensions, the other being the pentachoric bipyramid.

Two hexadecachoric pyramids can be attached at their bases to form a regular triacontaditeron. A hexadecachoric pyramid can be further cut in half to produce two octahedral scalenes.

Apart from being a point atop hexadecachoron, it has an alternate segmentochoron representation as a tetrahedron atop gyro pentachoron seen as a tetrahedral pyramid.

It appears as a facet of the scaliform tridiminished icosiheptaheptacontadipeton.

Vertex coordinates[edit | edit source]

The vertices of a hexadecachoric pyramid of edge length 1 are given by:

with all permutations of the first 4 coordinates of:

External links[edit | edit source]