Icosahedron-great dodecahedron morpher

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${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Volume${\displaystyle {\frac {15+7{\sqrt {5}}}{12}}\approx 2.55437}$
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: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
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), ${\displaystyle 1-{\frac {{\sqrt {5}}-1}{2}}}$ (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

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