# Octagonally tetrablended truncated tesseract

Octagonally tetrablended truncated tesseract
Rank4
TypeScaliform
Notation
Bowers style acronymOtbott
Elements
Cells64 tetrahedra
16 blends of 2 truncated cubes
Faces256 triangles
64 octagons
Edges256 3-fold
128 4-fold
Vertices128
Vertex figureButterfly wedge, edge lengths 2+2 (long butterfly edges) and 1 (remaining edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+3{\sqrt {2}}}{2}}}\approx 2.14973}$
Hypervolume0
Related polytopes
RegimentOtbott
ConjugateOctagonally tetrablended quasitruncated tesseract
Abstract & topological properties
Euler characteristic-16
OrientableYes
Properties
SymmetryI2(8)≀S2, order 512
ConvexNo
NatureTame

The octagonally tetrablended truncated tesseract or otbott is a nonconvex scaliform polychoron that consists of 64 regular tetrahedra and 16 blends of 2 truncated cubes. 2 tetrahedra and 4 blends of 2 truncated cubes join at each vertex.

It can be constructed as a blend of 4 truncated tesseracts in the same way ondip is constructed as a blend of 4 sidpith. Its vertex figure is in turn a blend of two vertex figures of the truncated tesseract. It has the same symmetry as the octagonal duoprism.

## Vertex coordinates

The vertices of an octagonally tetrablended truncated tesseract of edge length 1 are given by all permutations of:

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

along with all permutations of the first two and/or last two coordinates of:

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

The first set of vertices are identical to the vertices of an inscribed truncated tesseract.