Rank4
TypeSegmentotope
Notation
Bowers style acronymHexpy
Coxeter diagramoo4oo3oo3ox&#x
Elements
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${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Hypervolume${\displaystyle {\frac {\sqrt {2}}{60}}\approx 0.023570}$
HeightPoint atop hex: ${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
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

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

• ${\displaystyle \left(0,\,0,\,0,\,0,\,{\frac {\sqrt {2}}{2}}\right),}$

with all permutations of the first 4 coordinates of:

• ${\displaystyle \left(0,\,0,\,0,\,\pm {\frac {\sqrt {2}}{2}},\,0\right).}$