❴12,12∣3❵

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{12,12∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{12,12∣3}
Elements
FacesN  dodecagons
Edges6N 
VerticesN 
Vertex figureSkew dodecagon
HolesTriangles
Measures (edge length 1)
Circumradius
Related polytopes
Dual{12,12∣3}
Convex hullCyclotruncated hexagonal tiling-triangular tiling honeycomb
Abstract & topological properties
Flag count24N 
Schläfli type{12,12}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {12,12∣3} is a paracompact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are exactly the dodecagonal faces of the cyclotruncated hexagonal tiling-triangular tiling honeycomb. It is a self-dual polyhedron, and it also shares a symmetry group with another hyperbolic regular skew apeirohedron: {6,6∣6}.

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