❴6,8∣4❵

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{6,8∣4}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{6,8∣4}
Elements
Faces4N  hexagons
Edges12N 
Vertices3N 
Vertex figureSkew octagon, edge length
HolesSquares
Measures (edge length 1)
Circumradius
Related polytopes
Dual{8,6∣4}
φ 2 Square tiling
Convex hullcyclotruncated octahedral-square tiling honeycomb
Abstract & topological properties
Flag count48N 
Schläfli type{6,8}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {6,8∣4} is a paracompact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the hexagonal faces of the cyclotruncated octahedral-square 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