❴12,10∣3❵

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{12,10∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{12,10∣3}
Elements
Faces5N  dodecagons
Edges30N 
Vertices6N 
Vertex figureSkew decagon
HolesTriangles
Related polytopes
Dual{10,12∣3}
Convex hullCyclotruncated icosahedral-hexagonal tiling honeycomb
Abstract & topological properties
Flag count120N 
Schläfli type{12,10}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

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