Tridiminished icosahedron (EntityTopic, 10)

From Hi.gher. Space

The tridiminished icosahedron, abbreviated TDI, is the 63rd Johnson solid, J63. It suddenly became important when the bixylodiminished hydrochoron was discovered. It is the only CRF 3D member of the family of ursatopes, and appears as cells in the majority of the higher-dimensional ones.

Relationship with J83

J83 can be constructed as a sort of informal expansion of J63. See the tridiminished rhodoperihedron page for the visualisation.

Equations

  • The hypervolumes of a tridiminished icosahedron with side length l are given by:
total edge length = 15l
surface area = 14 · (3√(25+10√5) + 5√3) · l2
volume = (15+7√5)24 · l3

Incidence matrix

Dual: J63 dual

#TXIDVaVbVcEaEbEcEd3a5a3b3cTypeName
0 Va = point ; top vertices
1 Vb = point ; mid vertices
2 Vc = point ; bot vertices
3 Ea 200 = digon ; top to pen
4 Eb 110 = digon ; pen to pen
5 Ec 011 = digon ; pen to lat
6 Ed 002 = digon ; lat to bot
7 3a 3003000 = triangle ; top
8 5a 2211220 = pentagon ; pen
9 3b 0120021 = triangle ; lat
10 3c 0030003 = triangle ; bot
11 C1a 33333631331 = tridiminished icosahedron ;

Usage as facets


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