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An apeirogonal hosohedron is a tiling composed of infinitely many digonal faces, all sharing the same two vertices. In normal Euclidean space, it is degenerate.

See Also

$ \{e,v\} $ $ \{e,1\} $ $ \{e,2\} $ $ \{e,3\} $ $ \{e,4\} $ $ \{e,5\} $ $ \{e,6\} $ $ \{e,7\} $ $ \{e,8\} $

...

$ \{e,\aleph_0\} $
$ \{1,v\} $ $ \{1,1\} $

Monogonal monohedron

$ \{1,2\} $

Monogonal Dihedron

$ \{1,3\} $

Monogonal trihedron

$ \{1,4\} $

Monogonal tetrahedron

$ \{1,5\} $

Monogonal pentahedron

$ \{1,6\} $

Monogonal hexahedron

$ \{1,7\} $

Monogonal heptahedron

$ \{1,8\} $

Monogonal octahedron

...

$ \{1,\aleph_0\} $

N/A

$ \{2,v\} $ $ \{2,1\} $

Monogonal hosohedron

$ \{2,2\} $

Digonal hosohedron

$ \{2,3\} $

Trigonal hosohedron

$ \{2,4\} $

Square hosohedron

$ \{2,5\} $

Pentagonal hosohedron

$ \{2,6\} $

Hexagonal hosohedron

$ \{2,7\} $

Heptagonal hosohedron

$ \{2,8\} $

Octagonal hosohedron

...

$ \{2,\aleph_0\} $

Apeirogonal hosohedron

$ \{3,v\} $ $ \{3,1\} $

N/A

$ \{3,2\} $

Triangular dihedron

$ \{3,3\} $

Tetrahedron

$ \{3,4\} $

Octahedron

$ \{3,5\} $

Icosahedron

$ \{3,6\} $

Triangular tiling

$ \{3,7\} $

Order-7 triangular tiling

$ \{3,8\} $

Order-8 triangular tiling

...

$ \{3,\aleph_0\} $

Infinite-order triangular tiling

$ \{4,v\} $ $ \{4,1\} $

N/A

$ \{4,2\} $

Square dihedron

$ \{4,3\} $

Cube

$ \{4,4\} $

Square tiling

$ \{4,5\} $

Order-5 square tiling

$ \{4,6\} $

Order-6 square tiling

$ \{4,7\} $

Order-7 square tiling

$ \{4,8\} $

Order-8 square tiling

...

$ \{4,\aleph_0\} $

Infinite-order square tiling

$ \{5,v\} $ $ \{5,1\} $

N/A

$ \{5,2\} $

Pentagonal dihedron

$ \{5,3\} $

Dodecahedron

$ \{5,4\} $

Order-4 pentagonal tiling

$ \{5,5\} $

Order-5 pentagonal tiling

$ \{5,6\} $

Order-6 pentagonal tiling

$ \{5,7\} $

Order-7 pentagonal tiling

$ \{5,8\} $

Order-8 pentagonal tiling

...

$ \{5,\aleph_0\} $

Infinite-order pentagonal tiling

$ \{6,v\} $ $ \{6,1\} $

N/A

$ \{6,2\} $

Hexagonal dihedron

$ \{6,3\} $

Hexagonal tiling

$ \{6,4\} $

Order-4 hexagonal tiling

$ \{6,5\} $

Order-5 hexagonal tiling

$ \{6,6\} $

Order-6 hexagonal tiling

$ \{6,7\} $

Order-7 hexagonal tiling

$ \{6,8\} $

Order-8 hexagonal tiling

...

$ \{6,\aleph_0\} $

Infinite-order hexagonal tiling

$ \{7,v\} $ $ \{7,1\} $

N/A

$ \{7,2\} $

Heptagonal dihedron

$ \{7,3\} $

Order-3 heptagonal tiling

$ \{7,4\} $

Order-4 heptagonal tiling

$ \{7,5\} $

Order-5 heptagonal tiling

$ \{7,6\} $

Order-6 heptagonal tiling

$ \{7,7\} $

Order-7 heptagonal tiling

$ \{7,8\} $

Order-8 heptagonal tiling

...

$ \{7,\aleph_0\} $

Infinite-order heptagonal tiling

$ \{8,v\} $ $ \{8,1\} $

N/A

$ \{8,2\} $

Octagonal dihedron

$ \{8,3\} $

Order-3 octagonal tiling

$ \{8,4\} $

Order-4 octagonal tiling

$ \{8,5\} $

Order-5 octagonal tiling

$ \{8,6\} $

Order-6 octagonal tiling

$ \{8,7\} $

Order-7 octagonal tiling

$ \{8,8\} $

Order-8 octagonal tiling

...

$ \{8,\aleph_0\} $

Infinite-order octagonal tiling

...

...

...

...

...

...

...

...

...

$ \emptyset $

...

$ \{\aleph_0,v\} $ $ \{\aleph_0,1\} $

N/A

$ \{\aleph_0,2\} $

Apeirogonal dihedron

$ \{\aleph_0,3\} $

Order-3 apeirogonal tiling

$ \{\aleph_0,4\} $

Order-4 apeirogonal tiling

$ \{\aleph_0,5\} $

Order-5 apeirogonal tiling

$ \{\aleph_0,6\} $

Order-6 apeirogonal tiling

$ \{\aleph_0,7\} $

Order-7 apeirogonal tiling

$ \{\aleph_0,8\} $

Order-8 apeirogonal tiling

...

$ \{\aleph_0,\aleph_0\} $

Infinite-order apeirogonal tiling

$ \{2,\aleph_0\} $ $ \{3,\aleph_0\} $ $ \{4,\aleph_0\} $ $ \{5,\aleph_0\} $ $ \{6,\aleph_0\} $ $ \{7,\aleph_0\} $ $ \{8,\aleph_0\} $ ... $ \{\aleph_0,\aleph_0\} $
Apeirogonal hosohedron Infinite-order triangular tiling Infinite-order square tiling Infinite-order pentagonal tiling Infinite-order hexagonal tiling Infinite-order heptagonal tiling Infinite-order octagonal tiling ... Infinite-order apeirogonal tiling