Acronym siphina
Name siphin alterprism,
medial segment of sochax
Circumradius sqrt(7)/2 = 1.322876
Lace city
in approx. ASCII-art
H   r   R   h		-- x3o3o *b3o3x (siphin)
             
h   R   r   H		-- o3o3x *b3o3x (alt. siphin)

|   |   |   +-- x3o3o *b3o3o (hin)
|   |   +------ xo3oo3xx *b3ox&#x (rita)
|   +---------- ox3oo3xx *b3xo&#x (alt. rita)
+-------------- o3o3x *b3o3o (alt. hin)

where:
H = x3o3o *b3o (hex)
h = o3o3o *b3x (gyro hex)
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 coord., all even changes of sign
Confer
uniform relative:
sochax  
related segmentopeta:
hinasiphin   ritas  
general polytopal classes:
segmentopeta   scaliform  

Incidence matrix according to Dynkin symbol

xo3oo3ox *b3oo3xx&#x   → height = 1/sqrt(2) = 0.707107
(siphin || alt. siphin)

o.3o.3o. *b3o.3o.    & | 160 |   6   4   4 |  12  12   6  18  12 |   4   4  12   6   4  16   6  36  12 |  1  4  4  1  4   5  16  12  18  4 | 1  1  4  5  6
-----------------------+-----+-------------+---------------------+-------------------------------------+-----------------------------------+--------------
x. .. ..    .. ..    & |   2 | 480   *   * |   4   2   0   2   0 |   2   2   4   1   0   4   1   4   0 |  1  2  2  0  2   2   4   2   2  0 | 1  1  2  2  1
.. .. ..    .. x.    & |   2 |   * 320   * |   0   3   3   0   3 |   0   0   3   3   3   0   0   9   6 |  0  1  3  1  0   0   4   3   9  3 | 1  0  1  4  3
oo3oo3oo *b3oo3oo&#x   |   2 |   *   * 320 |   0   0   0   6   3 |   0   0   0   0   0   6   3  12   3 |  0  0  0  0  3   2   6   6   6  1 | 0  1  3  2  3
-----------------------+-----+-------------+---------------------+-------------------------------------+-----------------------------------+--------------
x.3o. ..    .. ..    & |   3 |   3   0   0 | 640   *   *   *   * |   1   1   1   0   0   1   0   0   0 |  1  1  1  0  1   1   1   0   0  0 | 1  1  1  1  0
x. .. ..    .. x.    & |   4 |   2   2   0 |   * 480   *   *   * |   0   0   2   1   0   0   0   2   0 |  0  1  2  0  0   0   2   1   2  0 | 1  0  1  2  1
.. .. ..    o.3x.    & |   3 |   0   3   0 |   *   * 320   *   * |   0   0   0   1   2   0   0   0   2 |  0  0  2  1  0   0   0   0   3  2 | 1  0  0  3  1
xo .. ..    .. ..&#x & |   3 |   1   0   2 |   *   *   * 960   * |   0   0   0   0   0   2   1   2   0 |  0  0  0  0  2   1   2   2   1  0 | 0  1  2  1  1
.. .. ..    .. xx&#x   |   4 |   0   2   2 |   *   *   *   * 480 |   0   0   0   0   0   0   0   4   2 |  0  0  0  0  0   0   2   2   4  1 | 0  0  1  2  2
-----------------------+-----+-------------+---------------------+-------------------------------------+-----------------------------------+--------------
x.3o.3o.    .. ..    &    4 |   6   0   0 |   4   0   0   0   0 | 160   *   *   *   *   *   *   *   * |  1  1  1  0  1   0   0   0   0  0 | 1  1  1  0  0
x.3o. .. *b3o. ..    &    4 |   6   0   0 |   4   0   0   0   0 |   * 160   *   *   *   *   *   *   * |  1  0  2  0  0   1   0   0   0  0 | 1  1  0  1  0
x.3o. ..    .. x.    &    6 |   6   3   0 |   2   3   0   0   0 |   *   * 320   *   *   *   *   *   * |  0  1  1  0  0   0   1   0   0  0 | 1  0  1  1  0
x. .. ..    o.3x.    &    6 |   3   6   0 |   0   3   2   0   0 |   *   *   * 160   *   *   *   *   * |  0  0  1  0  0   0   0   0   2  0 | 1  0  0  2  1
.. o. .. *b3o.3x.    &    4 |   0   6   0 |   0   0   4   0   0 |   *   *   *   * 160   *   *   *   * |  0  0  0  1  0   0   0   0   0  1 | 1  0  0  2  0
xo3oo ..    .. ..&#x &    4 |   3   0   3 |   1   0   0   3   0 |   *   *   *   *   * 640   *   *   * |  0  0  0  0  1   1   1   0   0  0 | 0  1  1  1  0
xo .. ox    .. ..&#x      4 |   2   0   4 |   0   0   0   4   0 |   *   *   *   *   *   * 240   *   * |  0  0  0  0  2   0   0   2   0  0 | 0  1  2  0  1
xo .. ..    .. xx&#x &    6 |   2   3   4 |   0   1   0   2   2 |   *   *   *   *   *   *   * 960   * |  0  0  0  0  0   0   1   1   1  0 | 0  0  1  1  1
.. .. ..    oo3xx&#x      6 |   0   6   3 |   0   0   2   0   3 |   *   *   *   *   *   *   *   * 320 |  0  0  0  0  0   0   0   0   2  1 | 0  0  0  2  1
-----------------------+-----+-------------+---------------------+-------------------------------------+-----------------------------------+--------------
x.3o.3o. *b3o. ..    &    8 |  24   0   0 |  32   0   0   0   0 |   8   8   0   0   0   0   0   0   0 | 20  *  *  *  *   *   *   *   *  * | 1  1  0  0  0
x.3o.3o.    .. x.    &    8 |  12   4   0 |   8   6   0   0   0 |   2   0   4   0   0   0   0   0   0 |  * 80  *  *  *   *   *   *   *  * | 1  0  1  0  0
x.3o. .. *b3o.3x.    &   20 |  30  30   0 |  20  30  20   0   0 |   5  10  10   5   0   0   0   0   0 |  *  * 32  *  *   *   *   *   *  * | 1  0  0  1  0
.. o.3o. *b3o.3x.    &    5 |   0  10   0 |   0   0  10   0   0 |   0   0   0   0   5   0   0   0   0 |  *  *  * 32  *   *   *   *   *  * | 1  0  0  1  0
xo3oo3ox    .. ..&#x      8 |  12   0  12 |   8   0   0  24   0 |   2   0   0   0   0   8   6   0   0 |  *  *  *  * 80   *   *   *   *  * | 0  1  1  0  0
xo3oo .. *b3oo ..&#x &    5 |   6   0   4 |   4   0   0   6   0 |   0   1   0   0   0   4   0   0   0 |  *  *  *  *  * 160   *   *   *  * | 0  1  0  1  0
xo3oo ..    .. xx&#x &    8 |   6   4   6 |   2   3   0   6   3 |   0   0   1   0   0   2   0   3   0 |  *  *  *  *  *   * 320   *   *  * | 0  0  1  1  0
xo .. ox    .. xx&#x      8 |   4   4   8 |   0   2   0   8   4 |   0   0   0   0   0   0   2   4   0 |  *  *  *  *  *   *   * 240   *  * | 0  0  1  0  1
xo .. ..    oo3xx&#x &    9 |   3   9   6 |   0   3   3   3   6 |   0   0   0   1   0   0   0   3   2 |  *  *  *  *  *   *   *   * 320  * | 0  0  0  1  1
.. oo .. *b3oo3xx&#x      8 |   0  12   4 |   0   0   8   0   6 |   0   0   0   0   2   0   0   0   4 |  *  *  *  *  *   *   *   *   * 80 | 0  0  0  2  0
-----------------------+-----+-------------+---------------------+-------------------------------------+-----------------------------------+--------------
x.3o.3o. *b3o.3x.    &   80 | 240 160   0 | 320 240 160   0   0 |  80  80 160  80  80   0   0   0   0 | 10 40 16 16  0   0   0   0   0  0 | 2  *  *  *  *
xo3oo3ox *b3oo ..&#x     16 |  48   0  32 |  64   0   0  96   0 |  16  16   0   0   0  64  24   0   0 |  2  0  0  0  8  16   0   0   0  0 | * 10  *  *  *
xo3oo3ox    .. xx&#x     16 |  24   8  24 |  16  12   0  48  12 |   4   0   8   0   0  16  12  24   0 |  0  2  0  0  2   0   8   6   0  0 | *  * 40  *  *
xo3oo .. *b3oo3xx&#x &   25 |  30  40  20 |  20  30  30  30  30 |   0   5  10  10  10  20   0  30  20 |  0  0  1  1  0   5  10   0  10  5 | *  *  * 32  *
xo .. ox    oo3xx&#x     12 |   6  12  12 |   0   6   4  12  12 |   0   0   0   2   0   0   3  12   4 |  0  0  0  0  0   0   0   3   4  0 | *  *  *  * 80

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