❴6,6∣4❵

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{6,6∣4}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{6,6∣4}
Elements
FacesN  hexagons
Edges3N 
VerticesN 
Vertex figureSkew hexagon
HolesSquares
Measures (edge length 1)
Circumradiusi 
Related polytopes
ArmyCytoch
RegimentCytoch
Dual{6,6∣4}
Convex hullCyclotruncated octahedral-cubic honeycomb
Abstract & topological properties
Flag count12N 
Schläfli type{6,6}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {6,6∣4} is a compact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the hexagonal faces of the cyclotruncated octahedral-cubic honeycomb. It is a self-dual polyhedron, and it also shares a symmetry group with another hyperbolic regular skew apeirohedron: {8,8∣3}.

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