# Grand hexadecagonal prismatic blend

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Grand hexadecagonal prismatic blend
Rank3
TypeOrbiform
Notation
Bowers style acronymGahadpib
Elements
Faces6 great hexadecagrams, 36 squares
Edges24+24+24+48
Vertices24+48
Vertex figures24 (4.16/7.4/3.16/9)
48 (4.4.16/7)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2+{\sqrt {2}}-{\sqrt {\frac {10+7{\sqrt {2}}}{2}}}}}\approx 0.50980}$
Dihedral angles4-4 (prism laces): 22.5°
4-16 (prism bases): 90°
4-16 (at edges of blended-away squares): 67.5°
Central density21
Related polytopes
ConjugatesSmall hexadecagonal prismatic blend, Medial hexadecagonal prismatic blend, Great hexadecagonal prismatic blend
Convex coreTetrakis chamfered cube
Abstract & topological properties
Flag count480
Euler characteristic–6
OrientableNo
Genus8
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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

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

## Vertex coordinates

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

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