Great icosahedron bomb

Great icosahedron bomb
(OFF file)
Rank	3
Type	Orbiform
Notation
Bowers style acronym	Gib
Elements
Faces	1+3+3+6 triangles, 3 pentagrams
Edges	3+3+3+6+6+6
Vertices	3+3+3+3
Vertex figures	3 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	${\sqrt {\frac {5-{\sqrt {5}}}{8}}}\approx 0.58779$
Dihedral angles	3-5/2 #1: $\arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }$
	3-3: $\arccos \left({\frac {\sqrt {5}}{3}}\right)\approx 41.81031^{\circ }$
	3-5/2 #2: $\arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }$
Related polytopes
Army	Ike, edge length ${\frac {{\sqrt {5}}-1}{2}}$
Conjugate	Icosahedron bomb
Abstract & topological properties
Flag count	108
Orientable	No
Properties
Symmetry	A2×I, order 6
Convex	No
Nature	Tame

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.

External links

• Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#13 under sissid).