# Gyrated blend of truncated cubes

Gyrated blend of truncated cubes
Rank3
Notation
Bowers style acronymTutic
Elements
Faces8 octagons, 16 triangles
Edges8+16+32
Vertices16+16
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7+4{\sqrt {2}}}}{2}}\approx 1.77882}$
Central density0
Related polytopes
ConjugateGyrated blend of quasitruncated hexahedra
Abstract & topological properties
Euler characteristic0
OrientableYes
Genus1
Properties
SymmetryI2(8)×A1, order 32
ConvexNo

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

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

and all permutations of

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