Square biantiprismatic ring (EntityTopic, 19)

From Hi.gher. Space

The square biantiprismic ring is a member of the infinite family of biantiprismatic rings, which are 4D CRF polychora. It consists of a 3-membered ring containing two square antiprisms and a cube, flanked by a circle of 4 tetrahedra and 4 square pyramids.

Cartesian coordinates

Cube:

(±1, ±1, ±1, 0)

Square:

(±√2, 0, 0, H)
(0, ±√2, 0, H)

where H = √(2√2 - 1).

Incidence matrix

Dual: (dual of square biantiprismatic ring)

#TXIDVaVbEaEbEcEd4a4b3a3b3c4cC1aC2aC3aC4aTypeName
0 Va = point ; end
1 Vb = point ; mid
2 Ea 20 = digon ; end
3 Eb 20 = digon ; side
4 Ec 11 = digon ; lace
5 Ed 02 = digon ; mid
6 4a 404000 = square ; end
7 4b 402200 = square ; side
8 3a 211020 = triangle ; lace end
9 3b 210120 = triangle ; lace side
10 3c 120021 = triangle ; lace mid
11 4c 040004 = square ; mid
12 C1a 444084104041 = square antiprism ;
13 C2a 808400240000 = cube ;
14 C3a 412240012200 = square pyramid ;
15 C4a 220141000220 = tetrahedron ;
16 H4.1a 84841642488812144 = square biantiprismatic ring ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.

Additional images

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Software models