Brick symmetric icosahedron faceting

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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
Volume
Dihedral angles3-3:
 3-5 #1:
 5-5:
 3-5 #2:
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[edit | edit source]

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

External links[edit | edit source]