# Octagonally tetrablended quasitruncated tesseract

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

Octagonally tetrablended quasitruncated tesseract
Rank4
TypeScaliform
Notation
Bowers style acronymOtbaquitit
Elements
Cells64 tetrahedra
16 blends of 2 quasitruncated cubes
Faces256 triangles
64 octagrams
Edges256 3-fold
128 4-fold
Vertices128
Vertex figureButterfly wedge, edge lengths 2-2 (short butterfly edges) and 1 (remaining edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5-3{\sqrt {2}}}{2}}}\approx 0.615370}$
Hypervolume0
Related polytopes
RegimentOtbaquitit
ConjugateOctagonally tetrablended truncated tesseract
Abstract & topological properties
Euler characteristic-16
OrientableYes
Properties
SymmetryI2(8)≀S2, order 512
ConvexNo
NatureTame

It can be constructed as a blend of 4 quasitruncated 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 quasitruncated 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:

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

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

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

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