Icosahedron-great dodecahedron morpher

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Icosahedron-great dodecahedron morpher
Rank3
TypeOrbiform
Notation
Bowers style acronymIgdom
Elements
Faces5+5 triangles, 1+5 pentagons
Edges5+5+5+5+10
Vertices1+1+5+5
Vertex figures1 pentagon, edge length 1
 1 pentagram, edge length (1+5)/2
 5 nonconvex pentagons, edge lengths 1, 1, (1+5)/2, 1, (1+5)/2
 5 nonconvex pentagons, edge lengths 1, (1+5)/2, (1+5)/2, 1, (1+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3-3:
 3-5:
 5-5:
Number of external pieces45
Level of complexity28
Related polytopes
ArmyIke
RegimentIke
ConjugateGreat icosahedron-small stellated dodecahedron morpher
Convex hullIcosahedron
Convex corePentagonal frustrum, edge lengths 1 (large base, sides), (small base)
Abstract & topological properties
Flag count120
Euler characteristic–2
OrientableYes
Genus2
SkeletonIcosahedral graph
Properties
SymmetryH2×I, order 10
ConvexNo
NatureTame

The icosahedron-great dodecahedron morpher or igdom, also called the ike-gad morpher, is a nonconvex orbiform polyhedron and an edge faceting of the icosahedron. Its faces are 5+5 triangles and 1+5 pentagons.

It is named as such because one vertex is surrounded by 5 triangles like a vertex of the icosahedron, while the opposing vertex is surrounded by 5 pentagons like a vertex of the great dodecahedron. It uses half the faces of each of these regular polyhedra.

It appears as a cell of the small hemiswirlprism.

Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the icosahedron.

Gallery[edit | edit source]

External links[edit | edit source]