❴12,6∣3❵

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{12,6∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{12,6∣3}
Elements
FacesN  dodecagons
Edges3N 
Vertices2N 
Vertex figureSkew hexagon, edge length
HolesTriangles
Related polytopes
Dual{6,12∣3}
φ 2 Tetrahedron
Convex hullCyclotruncated hexagonal tiling-tetrahedral honeycomb
Abstract & topological properties
Flag count12N 
Schläfli type{12,6}
OrientableYes
Genus
Properties
Symmetry[(6,3,3,3)]
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {12,6∣3} is a paracompact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the dodecagonal faces of the cyclotruncated hexagonal tiling-tetrahedral 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