# Brick symmetric icosahedron faceting

Brick symmetric icosahedron faceting
Rank3
TypeOrbiform
Notation
Bowers style acronymBissif
Elements
Faces4+4 triangles, 4 pentagons
Edges2+2+2+8+8
Vertices4+4+4
Vertex figures4 nonconvex pentagons, edge lengths 1, 1, (1+5)/2, 1, (1+5)/2
4 isosceles triangles, edge lengths 1, 1, (1+5)/2
4 isosceles triangles, edge lengths 1, (1+5)/2, (1+5)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Volume${\displaystyle {\frac {11+5{\sqrt {5}}}{12}}\approx 1.84836}$
Dihedral angles3-3: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{3}}\right)\approx 138.18969^{\circ }}$
3-5 #1: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
5-5: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
3-5 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Central density1
Number of external pieces16
Level of complexity13
Related polytopes
ConjugateBrick-symmetric great icosahedron faceting
Convex hullIcosahedron
Convex coreDigonal orthobicupola, oxo2xfx&#xt
Abstract & topological properties
Flag count88
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryK3, order 8
ConvexNo
NatureTame

The brick symmetric icosahedron faceting or bissif, also called the spaceship, is an orbiform polyhedron. It consists of 8 triangles and 4 pentagons. As its name suggests, it is a faceting of the icosahedron.

It appears as a cell of the small digonal swirlprism.

## Vertex coordinates

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