Small hexadecagonal prismatic blend

Small hexadecagonal prismatic blend
(OFF file)
Rank	3
Type	Orbiform
Space	Spherical
Notation
Bowers style acronym	Shadpib
Elements
Faces	6 hexadecagons, 36 squares
Edges	24+24+24+48
Vertices	24+48
Vertex figures	24 (4.16.4/3.16/15)
	48 (4.4.16)
Measures (edge length 1)
Circumradius	$\sqrt{2+\sqrt2+\sqrt{\frac{10+7\sqrt2}{2}}} \approx 2.56292$
Dihedral angles	4-4 (prism laces): 157.5°
	4-16 (prism bases): 90°
	4-16 (at edges of blended-away squares): 67.5°
Central density	3
Number of external pieces	90
Level of complexity	16
Related polytopes
Conjugates	Medial hexadecagonal prismatic blend, Great hexadecagonal prismatic blend, Grand hexadecagonal prismatic blend
Convex core	Cube
Abstract & topological properties
Flag count	480
Euler characteristic	–6
Orientable	No
Genus	8
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

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

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

Vertex coordinates

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

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