Acronym ritag rit, rit || gyro rit
Name rit atop gyro rit,
medial segment of hex-first siphin
Circumradius sqrt(13/8) = 1.274755
Lace city
in approx. ASCII-art
x3o3o  x3x3o  o3x3x  o3o3x
                          
                          
                          
o3o3x  o3x3x  x3x3o  x3o3o
Coordinates (1/sqrt(8); 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 3/sqrt(8))       & all permutations in all but first coord., all even changes of sign
Confer
uniform relative:
siphin
general polytopal classes:
segmentotera   scaliform  

This polyteron can be considered a partial Stott expansion of the hemipenteract. In fact, when considering the full symmetry of hin, then that expansion would result in siphin instead.


Incidence matrix according to Dynkin symbol

xo3oo3ox *b3xx&#x   → height = 1/sqrt(2) = 0.707107
(rit || gyro rit)

o.3o.3o. *b3o.    | 32  * |  3  3  3  0  0 |  3  3  3  6  3  6  0  0  0 | 1 3 1  3  3  6  1  3  3 0 0 0 | 1 1 3  3 1 0
.o3.o3.o *b3.o    |  * 32 |  0  0  3  3  3 |  0  0  0  3  6  6  3  3  3 | 0 0 0  1  3  3  3  3  6 1 1 3 | 0 1 1  3 3 1
------------------+-------+----------------+----------------------------+-------------------------------+-------------
x. .. ..    ..    |  2  0 | 48  *  *  *  * |  2  1  0  2  0  0  0  0  0 | 1 2 0  2  1  2  0  0  0 0 0 0 | 1 1 2  1 0 0
.. .. ..    x.    |  2  0 |  * 48  *  *  * |  0  1  2  0  0  2  0  0  0 | 0 2 1  0  0  2  0  2  1 0 0 0 | 1 0 2  1 1 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 96  *  * |  0  0  0  2  2  2  0  0  0 | 0 0 0  1  2  2  1  1  2 0 0 0 | 0 1 1  2 1 0
.. .. .x    ..    |  0  2 |  *  *  * 48  * |  0  0  0  0  2  0  2  0  1 | 0 0 0  0  1  0  2  0  2 1 0 2 | 0 1 0  1 2 1
.. .. ..    .x    |  0  2 |  *  *  *  * 48 |  0  0  0  0  0  2  0  2  1 | 0 0 0  0  0  1  0  2  2 0 1 2 | 0 0 1  1 2 1
------------------+-------+----------------+----------------------------+-------------------------------+-------------
x.3o. ..    ..    |  3  0 |  3  0  0  0  0 | 32  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0  0  0 0 0 0 | 1 1 1  0 0 0
x. .. ..    x.    |  4  0 |  2  2  0  0  0 |  * 24  *  *  *  *  *  *  * | 0 2 0  0  0  2  0  0  0 0 0 0 | 1 0 2  1 0 0
.. o. .. *b3x.    |  3  0 |  0  3  0  0  0 |  *  * 32  *  *  *  *  *  * | 0 1 1  0  0  0  0  1  0 0 0 0 | 1 0 1  0 1 0
xo .. ..    ..&#x |  2  1 |  1  0  2  0  0 |  *  *  * 96  *  *  *  *  * | 0 0 0  1  1  1  0  0  0 0 0 0 | 0 1 1  1 0 0
.. .. ox    ..&#x |  1  2 |  0  0  2  1  0 |  *  *  *  * 96  *  *  *  * | 0 0 0  0  1  0  1  0  1 0 0 0 | 0 1 0  1 1 0
.. .. ..    xx&#x |  2  2 |  0  1  2  0  1 |  *  *  *  *  * 96  *  *  * | 0 0 0  0  0  1  0  1  1 0 0 0 | 0 0 1  1 1 0
.. .o3.x    ..    |  0  3 |  0  0  0  3  0 |  *  *  *  *  *  * 32  *  * | 0 0 0  0  0  0  1  0  0 1 0 1 | 0 1 0  0 1 1
.. .o .. *b3.x    |  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  0  0  1  0 0 1 1 | 0 0 1  0 1 1
.. .. .x    .x    |  0  4 |  0  0  0  2  2 |  *  *  *  *  *  *  *  * 24 | 0 0 0  0  0  0  0  0  2 0 0 2 | 0 0 0  1 2 1
------------------+-------+----------------+----------------------------+-------------------------------+-------------
x.3o.3o.    ..      4  0 |  6  0  0  0  0 |  4  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  *  * * * * | 1 1 0  0 0 0
x.3o. .. *b3x.     12  0 | 12 12  0  0  0 |  4  6  4  0  0  0  0  0  0 | * 8 *  *  *  *  *  *  * * * * | 1 0 1  0 0 0
.. o.3o. *b3x.      4  0 |  0  6  0  0  0 |  0  0  4  0  0  0  0  0  0 | * * 8  *  *  *  *  *  * * * * | 1 0 0  0 1 0
xo3oo ..    ..&#x   3  1 |  3  0  3  0  0 |  1  0  0  3  0  0  0  0  0 | * * * 32  *  *  *  *  * * * * | 0 1 1  0 0 0
xo .. ox    ..&#x   2  2 |  1  0  4  1  0 |  0  0  0  2  2  0  0  0  0 | * * *  * 48  *  *  *  * * * * | 0 1 0  1 0 0
xo .. ..    xx&#x   4  2 |  2  2  4  0  1 |  0  1  0  2  0  2  0  0  0 | * * *  *  * 48  *  *  * * * * | 0 0 1  1 0 0
.. oo3ox    ..&#x   1  3 |  0  0  3  3  0 |  0  0  0  0  3  0  1  0  0 | * * *  *  *  * 32  *  * * * * | 0 1 0  0 1 0
.. oo .. *b3xx&#x   3  3 |  0  3  3  0  3 |  0  0  1  0  0  3  0  1  0 | * * *  *  *  *  * 32  * * * * | 0 0 1  0 1 0
.. .. ox    xx&#x   2  4 |  0  1  4  2  2 |  0  0  0  0  2  2  0  0  1 | * * *  *  *  *  *  * 48 * * * | 0 0 0  1 1 0
.o3.o3.x    ..      0  4 |  0  0  0  6  0 |  0  0  0  0  0  0  4  0  0 | * * *  *  *  *  *  *  * 8 * * | 0 1 0  0 0 1
.o3.o .. *b3.x      0  4 |  0  0  0  0  6 |  0  0  0  0  0  0  0  4  0 | * * *  *  *  *  *  *  * * 8 * | 0 0 1  0 0 1
.. .o3.x *b3.x      0 12 |  0  0  0 12 12 |  0  0  0  0  0  0  4  4  6 | * * *  *  *  *  *  *  * * * 8 | 0 0 0  0 1 1
------------------+-------+----------------+----------------------------+-------------------------------+-------------
x.3o.3o. *b3x.     32  0 | 48 48  0  0  0 | 32 24 32  0  0  0  0  0  0 | 8 8 8  0  0  0  0  0  0 0 0 0 | 1 * *  * * *
xo3oo3ox    ..&#x   4  4 |  6  0 12  6  0 |  4  0  0 12 12  0  4  0  0 | 1 0 0  4  6  0  4  0  0 1 0 0 | * 8 *  * * *
xo3oo .. *b3xx&#x  12  4 | 12 12 12  0  6 |  4  6  4 12  0 12  0  4  0 | 0 1 0  4  0  6  0  4  0 0 1 0 | * * 8  * * *
xo .. ox    xx&#x   4  4 |  2  2  8  2  2 |  0  1  0  4  4  4  0  0  1 | 0 0 0  0  2  2  0  0  2 0 0 0 | * * * 24 * *
.. oo3ox *b3xx&#x   4 12 |  0  6 12 12 12 |  0  0  4  0 12 12  4  4  6 | 0 0 1  0  0  0  4  4  6 0 0 1 | * * *  * 8 *
.o3.o3.x *b3.x      0 32 |  0  0  0 48 48 |  0  0  0  0  0  0 32 32 24 | 0 0 0  0  0  0  0  0  0 8 8 8 | * * *  * * 1
or
o.3o.3o. *b3o.    & | 64 |  3  3  3 |  3  3  3   9  6 |  1  3  1  4  3  9  3 | 1 1  4  3
--------------------+----+----------+-----------------+----------------------+----------
x. .. ..    ..    & |  2 | 96  *  * |  2  1  0   2  0 |  1  2  0  2  1  2  0 | 1 1  2  1
.. .. ..    x.    & |  2 |  * 96  * |  0  1  2   0  2 |  0  2  1  0  0  3  2 | 1 0  3  1
oo3oo3oo *b3oo&#x   |  2 |  *  * 96 |  0  0  0   4  2 |  0  0  0  2  2  4  1 | 0 1  2  2
--------------------+----+----------+-----------------+----------------------+----------
x.3o. ..    ..    & |  3 |  3  0  0 | 64  *  *   *  * |  1  1  0  1  0  0  0 | 1 1  1  0
x. .. ..    x.    & |  4 |  2  2  0 |  * 48  *   *  * |  0  2  0  0  0  2  0 | 1 0  2  1
.. o. .. *b3x.    & |  3 |  0  3  0 |  *  * 64   *  * |  0  1  1  0  0  0  1 | 1 0  2  0
xo .. ..    ..&#x & |  3 |  1  0  2 |  *  *  * 192  * |  0  0  0  1  1  1  0 | 0 1  1  1
.. .. ..    xx&#x   |  4 |  0  2  2 |  *  *  *   * 96 |  0  0  0  0  0  2  1 | 0 0  2  1
--------------------+----+----------+-----------------+----------------------+----------
x.3o.3o.    ..    &   4 |  6  0  0 |  4  0  0   0  0 | 16  *  *  *  *  *  * | 1 1  0  0
x.3o. .. *b3x.    &  12 | 12 12  0 |  4  6  4   0  0 |  * 16  *  *  *  *  * | 1 0  1  0
.. o.3o. *b3x.    &   4 |  0  6  0 |  0  0  4   0  0 |  *  * 16  *  *  *  * | 1 0  1  0
xo3oo ..    ..&#x &   4 |  3  0  3 |  1  0  0   3  0 |  *  *  * 64  *  *  * | 0 1  1  0
xo .. ox    ..&#x     4 |  2  0  4 |  0  0  0   4  0 |  *  *  *  * 48  *  * | 0 1  0  1
xo .. ..    xx&#x &   6 |  2  3  4 |  0  1  0   2  2 |  *  *  *  *  * 96  * | 0 0  1  1
.. oo .. *b3xx&#x     6 |  0  6  3 |  0  0  2   0  3 |  *  *  *  *  *  * 32 | 0 0  2  0
--------------------+----+----------+-----------------+----------------------+----------
x.3o.3o. *b3x.    &  32 | 48 48  0 | 32 24 32   0  0 |  8  8  8  0  0  0  0 | 2 *  *  *
xo3oo3ox    ..&#x     8 | 12  0 12 |  8  0  0  24  0 |  2  0  0  8  6  0  0 | * 8  *  *
xo3oo .. *b3xx&#x &  16 | 12 18 12 |  4  6  8  12 12 |  0  1  1  4  0  6  4 | * * 16  *
xo .. ox    xx&#x     8 |  4  4  8 |  0  2  0   8  4 |  0  0  0  0  2  4  0 | * *  * 24

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