Gyrated blend of truncated cubes

Gyrated blend of truncated cubes
Rank	3
Space	Spherical
Notation
Bowers style acronym	Tutic
Elements
Faces	8 octagons, 16 triangles
Edges	8+16+32
Vertices	16+16
Measures (edge length 1)
Circumradius	$\frac{\sqrt{7+4\sqrt{2}}}{2} \approx 1.77882$
Central density	0
Related polytopes
Conjugate	Gyrated blend of quasitruncated hexahedra
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Genus	1
Properties
Symmetry	I2(8)×A1, order 32
Convex	No

The gyrated blend of truncated cubes is a non-convex polyhedron with regular faces. It can be made by blending two truncated cubes.

It is the 8-8-3 acrohedron generated by Green's rules.

Vertex coordinates

The vertex coordinates for a gyrated blend of truncated cubes of unit length are given by

• $\left(\pm\frac{2+\sqrt{2}}{2}, 0, \pm\frac{1}{2}\right)$,
• $\left(0, \pm\frac{2+\sqrt{2}}{2}, \pm\frac{1}{2}\right)$,

and all permutations of

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

External links

• Klitzing, Richard. "tutic".