Rank3
TypeOrbiform
Notation
Elements
Edges24+24+24+48
Vertices24+48
Vertex figures24 (4.16/5.4/3.16/11)
48 (4.4.16/5)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2-{\sqrt {2}}-{\sqrt {\frac {10-7{\sqrt {2}}}{2}}}}}\approx 0.60134}$
Dihedral angles4-4 (prism laces): 67.5°
4-16/5 (prism bases): 90°
4-16/5 (at edges of blended-away squares): 22.5°
Central density15
Related polytopes
Convex coreTetrakis chamfered cube
Abstract & topological properties
Flag count480
Euler characteristic–6
OrientableNo
Genus8
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The great hexadecagonal prismatic blend is an orbiform polyhedron. It consists of 6 hexadecagrams and 36 squares. It can be obtained by blending 3 hexadecagrammic prisms together.

It appears as a cell in the small great prismatodistetracontoctachoron and the great great prismatodistetracontoctachoron.

## Vertex coordinates

The vertex coordinates for a great hexadecagonal prismatic blend of unit length are given by all permutations of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1-{\sqrt {2}}+{\sqrt {4-2{\sqrt {2}}}}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1-{\sqrt {2-{\sqrt {2}}}}}{2}},\,\pm {\frac {1-{\sqrt {2}}+{\sqrt {2-{\sqrt {2}}}}}{2}},\,\pm {\frac {1}{2}}\right).}$