# Small rhombicuboctahedron atop truncated cube

Small rhombicuboctahedron atop truncated cube
Rank4
TypeSegmentotope
Notation
Bowers style acronymSircoatic
Coxeter diagramxx4xo3ox&#x
Elements
Cells12 triangular prisms, 8 octahedra, 6 square cupolas, 1 small rhombicuboctahedron, 1 truncated cube
Faces8+8+24+24 triangles, 6+12+24 squares, 6 octagons
Edges12+24+24+24+48
Vertices24+24
Vertex figures24 square wedges, edge lengths 1 (base square) and 2 (top edge and sides)
24 skewed square pyramids, base edge lengths 1, side edge lengths 2+2 and 2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2+{\sqrt {2}}}}\approx 1.84776}$
Hypervolume${\displaystyle 4+3{\sqrt {2}}\approx 8.24264}$
Dichoral anglesOct–3–trip: 150°
Sirco–4–trip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
Squacu–4–trip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Sirco–3–oct: 120°
Squacu–3–oct: 120°
Sirco–4–squacu: 90°
Tic–8–squacu: 90°
Tic–3–oct: 60°
Height${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Central density1
Related polytopes
ArmySircoatic
RegimentSircoatic
DualDeltoidal icositetrahedral-triakis octahedral tegmoid
ConjugateQuasirhombicuboctahedron atop quasitruncated hexahedron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3×I, order 48
ConvexYes
NatureTame

Small rhombicuboctahedron atop truncated cube, or sircoatic, is a CRF segmentochoron (designated K-4.100 on Richard Klitzing's list). As the name suggests, it consists of a small rhombicuboctahedron and a truncated cube as bases, connected by 12 triangular prisms, 8 octahedra, and 6 square cupolas.

Two small rhombicuboctahedron atop truncated cube segmentochora can be attached to the bases of a truncated cubic prism to form a small rhombated tesseract, as the square cupolas of the caps fuse with the octagonal prisms of the truncated cubic prism to form further small rhombicuboctahedra.

## Vertex coordinates

The vertices of a small rhombicuboctahedron atop truncated cube segmentochoron of edge length 1 are given by:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,{\frac {\sqrt {2}}{2}}\right)}$ and all permutations of first three coordinates
• ${\displaystyle \left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,0\right)}$ and all permutations of first three coordinates