❴10,4∣3❵

From Polytope Wiki
Jump to navigation Jump to search
{10,4∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{10,4∣3}
Elements
Faces2N  decagons
Edges10N 
Vertices5N 
Vertex figureSkew square, edge length
HolesTriangles
Measures (edge length 1)
Circumradius
Related polytopes
ArmyBitih
RegimentBitih
Dual{4,10∣3}
φ 2 Triangular dihedron
Convex hullBitruncated icosahedral honeycomb
Abstract & topological properties
Flag count40N 
Schläfli type{10,4}
OrientableYes
Genus
Properties
Symmetry[[3,5,3]]
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {10,4∣3} is a compact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the decagonal faces of the bitruncated icosahedral honeycomb.

Bibliography[edit | edit source]

  • Garner, Cyril (1967), "Regular skew polyhedra in hyperbolic three-space" (PDF), Canadian Journal of Mathematics, 19, doi:10.4153/CJM-1967-106-9