# Great icosahedron bomb

Great icosahedron bomb
Rank3
TypeOrbiform
Notation
Bowers style acronymGib
Elements
Faces1+3+3+6 triangles, 3 pentagrams
Edges3+3+3+6+6+6
Vertices3+3+3+3
Vertex figures3 pentagrams, edge length 1
3 nonconvex pentagons, edge lengths 1, 1, (5–1)/2, 1, (5–1)/2
3 butterflies, edge lengths 1 and (5–1)/2
3 crossed isosceles trapezoids, edge lengths 1, 1, 1, (5–1)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\approx 0.58779}$
Dihedral angles3-5/2 #1: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
3-3: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{3}}\right)\approx 41.81031^{\circ }}$
3-5/2 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Related polytopes
ArmyIke, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
ConjugateIcosahedron bomb
Abstract & topological properties
Flag count108
OrientableNo
Properties
SymmetryA2×I, order 6
ConvexNo
NatureTame

The great icosahedron bomb, or gib, is an orbiform polyhedron and an edge-faceting of the small stellated dodecahedron. Its faces are 13 triangles and 3 pentagrams. It can be constructed by blending a great icosahedron with a semicupolaically faceted great icosahedron on the shared triangular faces.

## Vertex coordinates

Its vertices are the same as those of the small stellated dodecahedron.