Truncated octahedron atop great rhombicuboctahedron

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Truncated octahedron atop great rhombicuboctahedron
Rank4
TypeSegmentotope
Notation
Bowers style acronymToagirco
Coxeter diagramox4xx3xx&#x
Elements
Cells12 triangular prisms, 8 hexagonal prisms, 6 square cupolas, 1 truncated octahedron, 1 great rhombicuboctahedron
Faces24 triangles, 6+12+24+24 squares, 8+8 hexagons, 6 octagons
Edges12+24+24+24+24+48
Vertices24+48
Vertex figures24 isosceles trapezoidal pyramids, base edge lengths 1, 2, 2, 2; lateral edge lengths 2, 2, 3, 2+2
 48 irregular tetrahedra, edge lengths 1 (1), 2 (2), 3 (2), and 2+2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesHip–4–trip:
 Toe–6–hip: 150°
 Squacu–3–trip: 150°
 Squacu–4–hip:
 Toe–4–squacu: 135°
 Girco–4–squacu: 60°
 Girco–4–trip:
 Girco–6–hip: 30°
Height
Central density1
Related polytopes
ArmyToagirco
RegimentToagirco
DualTetrakis hexahedral-disdyakis dodecahedral tegmoid
ConjugateTruncated octahedron atop quasitruncated cuboctahedron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3×I, order 48
ConvexYes
NatureTame

Truncated octahedron atop great rhombicuboctahedron, or toagirco, is a CRF segmentochoron (designated K-4.149 on Richard Klitzing's list). As the name suggests, it consists of a truncated octahedron and a great rhombicuboctahedron as bases, connected by 12 triangular prisms, 8 hexagonal prisms, and 6 square cupolas.

It can be constructed as a cap of the prismatorhombated icositetrachoron, which can be obtained by attaching 8 of these segmentochora to the great rhombicuboctahedral cells of the great disprismatotesseractihexadecachoron.

Vertex coordinates[edit | edit source]

The vertices of a truncated octahedron atop great rhombicuboctahedron segmentochoron of edge length 1 are given by:

  • and all permutations of the first three coordinates,
  • and all permutations of the first three coordinates.

External links[edit | edit source]