Snub disphenoid (EntityTopic, 14)

From Hi.gher. Space

The snub disphenoid is the 84th Johnson solid, J84.

Cartesian coordinates

The Cartesian coordinates of the snub disphenoid, centered on the origin and with edge length 2, are:

(0, A, ±1)
(±C, B, 0)
(0, -B, ±C)
(±1, -A, 0)

where A=√u, B=√v, C=√w, and u, v, w are roots of the following cubic polynomials:

2u3 - u2 - 8u - 4 = 02 < u < 3
2v3 + 11v2 + 4v - 1 = 00 < v < 1
w3 - 17w2 + 64w - 64 = 01 < w < 2

The values of A, B, C are approximately:

A = 1.567861848465127
B = 0.411123131706519
C = 1.289168546448310

See also: Derivation of snub disphenoid coordinates

Images

(image)

Software models

Incidence matrix

Dual: digon-unpinched pentagonal prism

#TXIDVaVbEaEbEcEd3a3bTypeName
0 Va = point ;
1 Vb = point ;
2 Ea 20 = digon ;
3 Eb 11 = digon ;
4 Ec 11 = digon ;
5 Ed 02 = digon ;
6 3a 211110 = triangle ;
7 3b 120021 = triangle ;
8 C1a 44448284 = snub disphenoid ;

Usage as facets

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


Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind