❴8,12∣3❵

From Polytope Wiki
Jump to navigation Jump to search
{8,12∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{8,12∣3}
Elements
Faces3N  octagons
Edges12N 
Vertices2N 
Vertex figureSkew dodecagon, edge length
HolesTriangles
Related polytopes
Dual{12,8∣3}
φ 2 Triangular tiling
Convex hullCyclotruncated cubic-triangular tiling honeycomb
Abstract & topological properties
Flag count48N 
Schläfli type{8,12}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

{8,12∣3} is a regular skew polyhedron in 3-dimensional hyperbolic space. Its faces are exactly the octagonal faces of the cyclotruncated cubic-triangular tiling honeycomb. It has truncated cube and triangular tiling pseudocells.

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