Rectified tesseractihemioctachoron

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Rectified tesseractihemioctachoron
Rank4
TypeUniform
Notation
Bowers style acronymRatho
Coxeter diagram(x3o3x3o3/2*a)/2
Elements
Cells8 octahedra, 8 tetrahemihexahedra, 4 cuboctahedra
Faces32+32 triangles, 24 squares
Edges96
Vertices24
Vertex figureBowtie prism, base edge lengths 1 and 2, side edge length 1
Measures (edge length 1)
Circumradius1
Dichoral anglesOct–3–thah: 120°
 Thah–4–co: 90°
 Oct–3–co: 60°
Number of external pieces72
Level of complexity14
Related polytopes
ArmyIco
RegimentIco
ConjugateNone
Abstract & topological properties
Flag count1152
Euler characteristic–4
OrientableNo
Properties
SymmetryD4, order 192
ConvexNo
NatureTame

The rectified tesseractihemioctachoron, or ratho, is a nonconvex uniform polychoron that consists of 8 regular octahedra, 8 tetrahemihexahedra, and 4 cuboctahedra. Two of each type of cell join at each bowtie prismatic vertex. As the name suggests, it can be obtained by rectifying the tesseractihemioctachoron.

It is in the same regiment as the regular icositetrachoron.

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