❴12,8∣3❵

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{12,8∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{12,8∣3}
Elements
Faces2N  dodecagons
Edges12N 
Vertices3N 
Vertex figureSkew octagon, edge length
HolesTriangles
Related polytopes
Dual{8,12∣3}
φ 2 Octahedron
Convex hullCyclotruncated hexagonal tiling-octahedral honeycomb
Abstract & topological properties
Flag count48N 
Schläfli type{12,8}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

{12,8∣3} is a paracompact regular skew polyhedron in 3-dimensional hyperbolic space. Its faces are exactly the dodecagonal faces of the cyclotruncated hexagonal tiling-octahedral 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