❴6,10∣3❵

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{6,10∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{6,10∣3}
Elements
Faces5N  hexagons
Edges15N 
Vertices3N 
Vertex figureSkew decagon, edge length
HolesTriangles
Measures (edge length 1)
Circumradius
Related polytopes
Dual{10,6∣3}
φ 2 Icosahedron
Convex hullCyclotruncated tetrahedral-icosahedral honeycomb
Abstract & topological properties
Flag count60N 
Schläfli type{6,10}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {6,10∣3} is a compact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the hexagonal faces of the cyclotruncated tetrahedral-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