Acronym ritas
Name rit altersquarism,
cyclotetra-diminished sochax,
medial segment of siphina,
partial Stott expansion of hax
Circumradius sqrt(7)/2 = 1.322876
Lace city
in approx. ASCII-art
r   R		-- xo3oo3xx *b3ox&#x (rita)
     
R   r		-- ox3oo3xx *b3xo&#x (alt. rita)

where:
R = o3o3x *b3x (rit)
r = x3o3x *b3o (gyro rit)
Coordinates (1/sqrt(8), 1/sqrt(8); 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 3/sqrt(8))     all permutations in one but first two coord.s, all even changes of sign
Confer
uniform relative:
sochax   hax  
related segmentopeta:
hinasiphin   siphina  
general polytopal classes:
segmentopeta   scaliform  

Incidence matrix according to Dynkin symbol

xoxo3oooo3oxox *b3xxxx&#xr   → all cyclical heights = 1/sqrt(2) = 0.707107

o...3o...3o... *b3o...     & | 128 |   3   3   6  1 |   3  3   3  18  12   9  3 |  1  3  1   8   6  18   6  12  18  3  3 | 1  2  8  6   5   9  12  3  6  1 | 2  5 1  3  3
-----------------------------+-----+----------------+---------------------------+----------------------------------------+---------------------------------+-------------
x... .... ....    ....     & |   2 | 192   *   *  * |   2  1   0   4   0   0  0 |  1  2  0   4   2   4   0   2   0  0  0 | 1  2  4  2   2   0   2  1  0  0 | 2  2 1  1  0
.... .... ....    x...     & |   2 |   * 192   *  * |   0  1   2   0   4   0  1 |  0  2  1   0   0   6   4   0   6  0  2 | 1  0  6  2   0   6   4  0  2  1 | 2  4 0  1  2
oo..3oo..3oo.. *b3oo..&#x  & |   2 |   *   * 384  * |   0  0   0   4   2   2  0 |  0  0  0   2   2   4   1   4   4  1  0 | 0  1  2  2   2   2   4  2  2  0 | 1  2 1  2  1
o.o.3o.o.3o.o. *b3o.o.&#x  & |   2 |   *   *   * 64 |   0  0   0   0   0   6  3 |  0  0  0   0   0   0   0   6  12  3  3 | 0  0  0  0   2   6   6  3  6  1 | 0  2 1  3  3
-----------------------------+-----+----------------+---------------------------+----------------------------------------+---------------------------------+-------------
x...3o... ....    ....     & |   3 |   3   0   0  0 | 128  *   *   *   *   *  * |  1  1  0   2   0   0   0   0   0  0  0 | 1  2  2  0   1   0   0  0  0  0 | 2  1 1  0  0
x... .... ....    x...     & |   4 |   2   2   0  0 |   * 96   *   *   *   *  * |  0  2  0   0   0   4   0   0   0  0  0 | 1  0  4  2   0   0   2  0  0  0 | 2  2 0  1  0
.... o... .... *b3x...     & |   3 |   0   3   0  0 |   *  * 128   *   *   *  * |  0  1  1   0   0   0   2   0   0  0  1 | 1  0  4  0   0   3   0  0  0  1 | 2  3 0  0  1
xo.. .... ....    ....&#x  & |   3 |   1   0   2  0 |   *  *   * 768   *   *  * |  0  0  0   1   1   1   0   1   0  0  0 | 0  1  1  1   1   0   1  1  0  0 | 1  1 1  1  0
.... .... ....    xx..&#x  & |   4 |   0   2   2  0 |   *  *   *   * 384   *  * |  0  0  0   0   0   2   1   0   2  0  0 | 0  0  2  1   0   2   2  0  1  0 | 1  2 0  1  2
ooo.3ooo.3ooo. *b3ooo.&#x  & |   3 |   0   0   2  1 |   *  *   *   *   * 384  * |  0  0  0   0   0   0   0   2   2  1  0 | 0  0  0  0   1   1   2  2  2  0 | 0  1 1  2  1
.... .... ....    x.x.&#x  & |   4 |   0   2   0  2 |   *  *   *   *   *   * 96 |  0  0  0   0   0   0   0   0   4  0  2 | 0  0  0  0   0   4   2  0  2  1 | 0  2 0  1  2
-----------------------------+-----+----------------+---------------------------+----------------------------------------+---------------------------------+-------------
x...3o...3o...    ....     &    4 |   6   0   0  0 |   4  0   0   0   0   0  0 | 32  *  *   *   *   *   *   *   *  *  * | 1  2  0  0   0   0   0  0  0  0 | 2  0 1  0  0
x...3o... .... *b3x...     &   12 |  12  12   0  0 |   4  6   4   0   0   0  0 |  * 32  *   *   *   *   *   *   *  *  * | 1  0  2  0   0   0   0  0  0  0 | 2  1 0  0  0
.... o...3o... *b3x...     &    4 |   0   6   0  0 |   0  0   4   0   0   0  0 |  *  * 32   *   *   *   *   *   *  *  * | 1  0  2  0   0   0   0  0  0  1 | 2  2 0  0  0
xo..3oo.. ....    ....&#x  &    4 |   3   0   3  0 |   1  0   0   3   0   0  0 |  *  *  * 256   *   *   *   *   *  *  * | 0  1  1  0   1   0   0  0  0  0 | 1  1 1  0  0
xo.. .... ox..    ....&#x  &    4 |   2   0   4  0 |   0  0   0   4   0   0  0 |  *  *  *   * 192   *   *   *   *  *  * | 0  1  0  1   0   0   0  1  0  0 | 1  0 1  1  0
xo.. .... ....    xx..&#x  &    6 |   2   3   4  0 |   0  1   0   2   2   0  0 |  *  *  *   *   * 384   *   *   *  *  * | 0  0  1  1   0   0   1  0  0  0 | 1  1 0  1  0
.... oo.. .... *b3xx..&#x  &    6 |   0   6   3  0 |   0  0   2   0   3   0  0 |  *  *  *   *   *   * 128   *   *  *  * | 0  0  2  0   0   2   0  0  0  0 | 1  2 0  0  1
.... .... oxo.    ....&#x  &    4 |   1   0   4  1 |   0  0   0   2   0   2  0 |  *  *  *   *   *   *   * 384   *  *  * | 0  0  0  0   1   0   1  1  0  0 | 0  1 1  1  0
.... .... ....    xxx.&#x  &    6 |   0   3   4  2 |   0  0   0   0   2   2  1 |  *  *  *   *   *   *   *   * 384  *  * | 0  0  0  0   0   1   1  0  1  0 | 0  1 0  1  1
oooo3oooo3oooo *b3oooo&#x       4 |   0   0   4  2 |   0  0   0   0   0   4  0 |  *  *  *   *   *   *   *   *   * 96  * | 0  0  0  0   0   0   0  2  2  0 | 0  0 1  2  1
.... o.o. .... *b3x.x.&#x  &    6 |   0   6   0  3 |   0  0   2   0   0   0  3 |  *  *  *   *   *   *   *   *   *  * 64 | 0  0  0  0   0   2   0  0  0  1 | 0  2 0  0  1
-----------------------------+-----+----------------+---------------------------+----------------------------------------+---------------------------------+-------------
x...3o...3o... *b3x...     &   32 |  48  48   0  0 |  32 24  32   0   0   0  0 |  8  8  8   0   0   0   0   0   0  0  0 | 4  *  *  *   *   *   *  *  *  * | 2  0 0  0  0
xo..3oo..3ox..    ....&#x  &    8 |  12   0  12  0 |   8  0   0  24   0   0  0 |  2  0  0   8   6   0   0   0   0  0  0 | * 32  *  *   *   *   *  *  *  * | 1  0 1  0  0
xo..3oo.. .... *b3xx..&#x  &   16 |  12  18  12  0 |   4  6   8  12  12   0  0 |  0  1  1   4   0   6   4   0   0  0  0 | *  * 64  *   *   *   *  *  *  * | 1  1 0  0  0
xo.. .... ox..    xx..&#x  &    8 |   4   4   8  0 |   0  2   0   8   4   0  0 |  0  0  0   0   2   4   0   0   0  0  0 | *  *  * 96   *   *   *  *  *  * | 1  0 0  1  0
.... ooo.3oxo.    ....&#x  &    5 |   3   0   6  1 |   1  0   0   6   0   3  0 |  0  0  0   2   0   0   0   3   0  0  0 | *  *  *  * 128   *   *  *  *  * | 0  1 1  0  0
.... ooo. .... *b3xxx.&#x  &    9 |   0   9   6  3 |   0  0   3   0   6   3  3 |  0  0  0   0   0   0   2   0   3  0  1 | *  *  *  *   * 128   *  *  *  * | 0  1 0  0  1
.... .... oxo.    xxx.&#x  &    8 |   2   4   8  2 |   0  1   0   4   4   4  1 |  0  0  0   0   0   2   0   2   2  0  0 | *  *  *  *   *   * 192  *  *  * | 0  1 0  1  0
xoxo .... oxox    ....&#xr      8 |   4   0  16  4 |   0  0   0  16   0  16  0 |  0  0  0   0   4   0   0   8   0  4  0 | *  *  *  *   *   *   * 48  *  * | 0  0 1  1  0
.... .... ....    xxxx&#x       8 |   0   4   8  4 |   0  0   0   0   4   8  2 |  0  0  0   0   0   0   0   0   4  2  0 | *  *  *  *   *   *   *  * 96  * | 0  0 0  1  1
.... o.o.3o.o. *b3x.x.&#x  &    8 |   0  12   0  4 |   0  0   8   0   0   0  6 |  0  0  2   0   0   0   0   0   0  0  4 | *  *  *  *   *   *   *  *  * 16 | 0  2 0  0  0
-----------------------------+-----+----------------+---------------------------+----------------------------------------+---------------------------------+-------------
xo..3oo.. ox.. *b3xx..&#x  &   64 |  96  96  96  0 |  64 48  64 192  96   0  0 | 16 16 16  64  48  96  32   0   0  0  0 | 2  8 16 24   0   0   0  0  0  0 | 4  * *  *  *
.... ooo.3oxo. *b3xxx.&#x  &   20 |  12  24  24  4 |   4  6  12  24  24  12  6 |  0  1  2   8   0  12   8  12  12  0  4 | 0  0  2  0   4   4   6  0  0  1 | * 32 *  *  *
xoxo3oooo3oxox    ....&#xr     16 |  24   0  48  8 |  16  0   0  96   0  48  0 |  4  0  0  32  24   0   0  48   0 12  0 | 0  4  0  0  16   0   0  6  0  0 | *  * 8  *  *
xoxo .... oxox    xxxx&#xr     16 |   8   8  32  8 |   0  4   0  32  16  32  4 |  0  0  0   0   8  16   0  16  16  8  0 | 0  0  0  4   0   0   8  2  4  0 | *  * * 24  *
.... oooo .... *b3xxxx&#x      12 |   0  12  12  6 |   0  0   4   0  12  12  6 |  0  0  0   0   0   0   4   0  12  3  2 | 0  0  0  0   0   4   0  0  3  0 | *  * *  * 32

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