❴10,12∣3❵

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{10,12∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{10,12∣3}
Elements
Faces6N  decagons
Edges30N 
Vertices5N 
Vertex figureSkew dodecagon
HolesTriangles
Related polytopes
Dual{12,10∣3}
Convex hullCyclotruncated dodecahedral-triangular tiling honeycomb
Abstract & topological properties
Flag count120N 
Schläfli type{10,12}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {10,12∣3} is a paracompact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the decagonal faces of the cyclotruncated dodecahedral-triangular tiling 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