Great icosahedron-small stellated dodecahedron morpher

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Great icosahedron-small stellated dodecahedron morpher
Rank3
TypeOrbiform
Notation
Bowers style acronymGissdom
Elements
Faces5+5 triangles, 1+5 pentagrams
Edges5+5+5+5+10
Vertices1+1+5+5
Vertex figures1 pentagram, edge length 1
 1 pentagon, edge length (5–1)/2
 5 nonconvex pentagons, edge lengths 1, 1, (5–1)/2, 1, (5–1)/2
 5 nonconvex pentagons, edge lengths 1, (5–1)/2, (5–1)/2, 1, (5–1)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles5/2–5/2:
 3–3:
 3-5/2:
Number of external pieces105
Level of complexity68
Related polytopes
ConjugateIcosahedron-great dodecahedron morpher
Convex hullIcosahedron, edge length (5–1)/2
Convex coreElongated pentagonal pyramid
Abstract & topological properties
Flag count120
Euler characteristic–2
OrientableYes
Genus2
Properties
SymmetryH2×I, order 10
ConvexNo
NatureTame

The great icosahedron-small stellated dodecahedron morpher or gissdom, also called the gike-sissid morpher, is a nonconvex orbiform polyhedron and an edge faceting of the small stellated dodecahedron. Its faces are 5+5 triangles and 1 pentagrams.

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

It appears as a cell of the great hemiswirlprism.

Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the small stellated dodecahedron.

Gallery[edit | edit source]

External links[edit | edit source]