# Tridiminished icosahedron (EntityTopic, 10)

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

 # TXID Type Name Va Vb Vc Ea Eb Ec Ed 3a 5a 3b 3c 0 Va = point ; top vertices 1 Vb = point ; mid vertices 2 Vc = point ; bot vertices 3 Ea 2 0 0 = digon ; top to pen 4 Eb 1 1 0 = digon ; pen to pen 5 Ec 0 1 1 = digon ; pen to lat 6 Ed 0 0 2 = digon ; lat to bot 7 3a 3 0 0 3 0 0 0 = triangle ; top 8 5a 2 2 1 1 2 2 0 = pentagon ; pen 9 3b 0 1 2 0 0 2 1 = triangle ; lat 10 3c 0 0 3 0 0 0 3 = triangle ; bot 11 C1a 3 3 3 3 3 6 3 1 3 3 1 = tridiminished icosahedron ;

## Usage as facets

 Notable Trishapes Regular: tetrahedron • cube • octahedron • dodecahedron • icosahedron Direct truncates: tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate Mesotruncates: stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron Snubs: snub staurohedron • snub rhodohedron Curved: sphere • torus • cylinder • cone • frustum • crind