# Brick-symmetric great icosahedron faceting

Brick-symmetric great icosahedron faceting
Rank3
TypeOrbiform
Notation
Bowers style acronymBisgif
Elements
Faces4+4 triangles, 4 pentagrams
Edges2+2+2+8+8
Vertices4+4+4
Vertex figures4 nonconvex pentagons, edge lengths 1, 1, (5–1)/2, 1, (5–1)/2
4 isosceles triangles, edge lengths 1, 1, (5–1)/2
4 isosceles triangles, edge lengths 1, (5–1)/2, (5–1)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\approx 0.58779}$
Volume${\displaystyle {\frac {5{\sqrt {5}}-11}{12}}\approx 0.015028}$
Dihedral angles5/2-5/2: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
3-5/2 #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: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Number of external pieces52
Level of complexity47
Related polytopes
ConjugateBrick-symmetric icosahedron faceting
Convex hullIcosahedron, edge length (5–1)/2
Convex coreDigonal orthobicupola
Abstract & topological properties
Flag count88
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryK3, order 8
ConvexNo
NatureTame

The brick-symmetric great icosahedron faceting, or bisgif is an orbiform polyhedron. It consists of 8 triangles and 4 pentagrams. As its name suggests, it is a faceting of the great icosahedron, and thus also of the small stellated dodecahedron.

It appears as a cell of the great digonal swirlprism.

## Vertex coordinates

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