Rank3
TypeOrbiform
SpaceSpherical
Notation
Elements
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${\displaystyle \sqrt{2+\sqrt2-\sqrt{\frac{10+7\sqrt2}{2}}} \approx 0.50980}$
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
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:

• ${\displaystyle \left(\pm\frac12,\,\pm\frac{-1-\sqrt2+\sqrt{4+2\sqrt2}}{2},\,\pm\frac12\right),}$
• ${\displaystyle \left(\pm\frac{\sqrt{2+\sqrt2}-1}{2},\,\pm\frac{1+\sqrt2-\sqrt{2+\sqrt2}}{2},\,\pm\frac12\right).}$