❴8,6∣4❵

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{8,6∣4}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{8,6∣4}
Elements
Faces3N  octagons
Edges12N 
Vertices4N 
Vertex figureSkew hexagon, edge length
HolesSquares
Measures (edge length 1)
Circumradius
Related polytopes
Dual{6,8∣4}
φ 2 Cube
Convex hullCyclotruncated square tiling-cubic honeycomb
Abstract & topological properties
Flag count48N 
Schläfli type{8,6}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

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