❴10,8∣3❵

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{10,8∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{10,8∣3}
Elements
Faces4N  decagons
Edges20N 
Vertices5N 
Vertex figureSkew octagon, edge length
HolesTriangles
Measures (edge length 1)
Circumradius
Related polytopes
Dual{8,10∣3}
φ 2 Octahedron
Convex hullCyclotruncated dodecahedral-octahedral honeycomb
Abstract & topological properties
Flag count80N 
Schläfli type{10,8}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {10,8∣3} is a compact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the decagonal faces of the cyclotruncated dodecahedral-octahedral 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