## FANDOM

953 Pages

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.

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

...

$\{e,\aleph_0\}$
$\{1,v\}$ $\{1,1\}$ $\{1,2\}$ $\{1,3\}$ $\{1,4\}$ $\{1,5\}$ $\{1,6\}$ $\{1,7\}$ $\{1,8\}$

...

$\{1,\aleph_0\}$

N/A

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

...

$\{2,\aleph_0\}$

Apeirogonal hosohedron

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

N/A

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

...

$\{3,\aleph_0\}$
$\{4,v\}$ $\{4,1\}$

N/A

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

...

$\{4,\aleph_0\}$
$\{5,v\}$ $\{5,1\}$

N/A

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

...

$\{5,\aleph_0\}$
$\{6,v\}$ $\{6,1\}$

N/A

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

...

$\{6,\aleph_0\}$
$\{7,v\}$ $\{7,1\}$

N/A

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

...

$\{7,\aleph_0\}$
$\{8,v\}$ $\{8,1\}$

N/A

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

...

$\{8,\aleph_0\}$

...

...

...

...

...

...

...

...

...

$\emptyset$

...

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

N/A

$\{\aleph_0,2\}$ $\{\aleph_0,3\}$ $\{\aleph_0,4\}$ $\{\aleph_0,5\}$ $\{\aleph_0,6\}$ $\{\aleph_0,7\}$ $\{\aleph_0,8\}$

...

$\{\aleph_0,\aleph_0\}$
$\{2,\aleph_0\}$ $\{3,\aleph_0\}$ $\{4,\aleph_0\}$ $\{5,\aleph_0\}$ $\{6,\aleph_0\}$ $\{7,\aleph_0\}$ $\{8,\aleph_0\}$ ... $\{\aleph_0,\aleph_0\}$
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