Acronym ...
Name hyperbolic rhombitetraoctagonal tiling
 
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Circumradius sqrt[1-2 sqrt(2)-2 sqrt[2+sqrt(2)]]/2 = 1.175154 i
Vertex figure [43,8]
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Incidence matrix according to Dynkin symbol

x4o8x   (N → ∞)

. . . | 8N |  2  2 |  1  2 1
------+----+-------+--------
x . . |  2 | 8N  * |  1  1 0
. . x |  2 |  * 8N |  0  1 1
------+----+-------+--------
x4o . |  4 |  4  0 | 2N  * *
x . x |  4 |  2  2 |  * 4N *
. o8x |  8 |  0  8 |  *  * N

xx4xx   (N → ∞)

. . . . | 8N |  1  1  1  1 |  1  1 1  1
--------+----+-------------+-----------
x . . . |  2 | 4N  *  *  * |  1  1 0  0
. x . . |  2 |  * 4N  *  * |  0  0 1  1
. . x . |  2 |  *  * 4N  * |  1  0 1  0
. . . x |  2 |  *  *  * 4N |  0  1 0  1
--------+----+-------------+-----------
x . x . |  4 |  2  0  2  0 | 2N  * *  *
x . . x |  4 |  2  0  0  2 |  * 2N *  *
. x4x . |  6 |  0  3  3  0 |  *  * N  *
. x . x |  4 |  0  2  0  2 |  *  * * 2N

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