❴4,8∣4❵

From Polytope Wiki
Jump to navigation Jump to search
{4,8∣4}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{4,8∣4}
Elements
Facessquares
Edges
Vertices
Vertex figureSkew octagon, edge length
HolesSquares
Related polytopes
Dual{8,4∣4}
φ 2 Square tiling
Convex hullSmall prismated order-4 square tiling honeycomb
Abstract & topological properties
Schläfli type{4,8}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {4,8∣4} is a paracompact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the square faces of the small prismated order-4 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