# Metabidiminished icosahedron

Metabidiminished icosahedron
Rank3
TypeCRF
Notation
Bowers style acronymMibdi
Coxeter diagramxfox oxfo&#xt
Elements
Faces2+2+2+4 triangles, 2 pentagons
Edges1+1+2+4+4+4+4
Vertices2+2+2+4
Vertex figures2+4 isosceles trapezoids, edge length 1, 1, 1, (1+5)/2
2 isosceles triangles, edge lengths 1, (1+5)/2, (1+5)/2
2 pentagons, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Volume${\displaystyle {\frac {5+2{\sqrt {5}}}{6}}\approx 1.57869}$
Dihedral angles3-3: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{3}}\right)\approx 138.18969^{\circ }}$
3-5: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
5-5: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Central density1
Number of external pieces12
Level of complexity20
Related polytopes
ArmyMibdi
RegimentMibdi
DualMetabistellated dodecahedron
ConjugateMetabireplenished great icosahedron
Abstract & topological properties
Flag count80
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK2×I, order 6
ConvexYes
NatureTame

The metabidiminished icosahedron is one of the 92 Johnson solids (J62). It consists of 2+2+2+4 triangles and 2 pentagons. It can be constructed by removing two non-opposite, non-adjacent vertices from a regular icosahedron.

## Vertex coordinates

A metabidiminished icosahedron of edge length 1 has the following vertices:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}},\,+{\frac {1}{2}},\,0\right),}$
• ${\displaystyle \left(0,\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left({\frac {1}{2}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{4}}\right).}$