Rank5
TypeUniform
Notation
Coxeter diagram(x3o3o3o3o3/2*b)/2 (/2)
Elements
Cells80 tetrahedra
Faces80 triangles
Edges40
Vertices10
Vertex figureTesseractihemioctachoron, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Diteral angle${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Related polytopes
ArmyTac
RegimentTac
CompanyTac
ConjugateNone
Abstract & topological properties
Flag count3840
OrientableNo
Properties
SymmetryD5, order 1920
Flag orbits2
ConvexNo
NatureTame

The hexadecahemidecateron, or hehad, is a uniform hemipolyteron. It has 16 regular pentachora and 5 central hexadecachora as facets, with 8 pentachora and 4 hexadecachora at each vertex in the form of a tesseractihemioctachoron. It is the 5D demicross.

It is a faceting of the triacontaditeron, analogous to how the tetrahemihexahedron is a faceting of the octahedron, and the tesseractihemioctachoron is a faceting of the hexadecachoron. It shares the triacontaditeron's vertices, edges, faces, and cells. The 16 pentachora are half of those of the triacontaditeron, while the hexadecachora are its original vertex figures.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the triacontaditeron.