Small rhombicuboctahedron atop truncated cube

Small rhombicuboctahedron atop truncated cube
(OFF file)
Rank	4
Type	Segmentotope
Notation
Bowers style acronym	Sircoatic
Coxeter diagram	xx4xo3ox&#x
Elements
Cells	12 triangular prisms, 8 octahedra, 6 square cupolas, 1 small rhombicuboctahedron, 1 truncated cube
Faces	8+8+24+24 triangles, 6+12+24 squares, 6 octagons
Edges	12+24+24+24+48
Vertices	24+24
Vertex figures	24 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	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Hypervolume	$4+3{\sqrt {2}}\approx 8.24264$
Dichoral angles	Oct–3–trip: 150°
	Sirco–4–trip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Squacu–4–trip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Sirco–3–oct: 120°
	Squacu–3–oct: 120°
	Sirco–4–squacu: 90°
	Tic–8–squacu: 90°
	Tic–3–oct: 60°
Height	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Central density	1
Related polytopes
Army	Sircoatic
Regiment	Sircoatic
Dual	Deltoidal icositetrahedral-triakis octahedral tegmoid
Conjugate	Quasirhombicuboctahedron atop quasitruncated hexahedron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3×I, order 48
Convex	Yes
Nature	Tame

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:

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

External links

• Klitzing, Richard. "sircoatic".