Acronym ...
Name hyperbolic trioctagonal tiling
 
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Circumradius sqrt[-1-sqrt(2)] = 1.553774 i
Vertex figure [(3,8)2]
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Incidence matrix according to Dynkin symbol

o3x8o   (N → ∞)

. . . | 12N |   4 |  2  2
------+-----+-----+------
. x . |   2 | 24N |  1  1
------+-----+-----+------
o3x . |   3 |   3 | 8N  *
. x8o |   8 |   8 |  * 3N

x3o3x4*a   (N → ∞)

. . .    | 12N |   2   2 |  1  2  1
---------+-----+---------+---------
x . .    |   2 | 12N   * |  1  1  0
. . x    |   2 |   * 12N |  0  1  1
---------+-----+---------+---------
x3o .    |   3 |   3   0 | 4N  *  *
x . x4*a |   8 |   4   4 |  * 3N  *
. o3x    |   3 |   0   3 |  *  * 4N

o3x8s   (N → ∞)

demi( . . . ) | 12N |   2   2 |  1  2  1
--------------+-----+---------+---------
demi( . x . ) |   2 | 12N   * |  1  1  0
sefa( . x8s ) |   2 |   * 12N |  0  1  1
--------------+-----+---------+---------
demi( o3x . ) |   3 |   3   0 | 4N  *  *
      . x8s      8 |   4   4 |  * 3N  *
sefa( o3x8s ) |   3 |   0   3 |  *  * 4N

starting figure: o3x8x

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