Acronym rita (old: ritag 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:
scaliform   segmentotera   lace simplices  

Note that hin well can be given within D4×Id subsymmetry (as being used in here below as a lace prism too) but also within A3×A1×A1 subsymmetry. Both representations allow as such for a partial Stott expansion. Thus an according acronym pexhin could be considered arbitrary. In 2021 it got applied to the latter reading though, as its formerly being used one, tutas, tends to conflict with the plural of tuta, while the one resulting by the in here being used representation, i.e. rita, was already an unconflicted acronym.

Starting from siphin the medial segment is rita and the medial segment thereof with respect to a perpendicular direction happens to be pexhin (tutas).


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

s2x3o3o4s

demi( . . . . . ) | 64 |  3  3  3 |  3  6  3   9  3 |  1  3  3  1  9  4  3 |  3 1 1  4
------------------+----+----------+-----------------+----------------------+----------
demi( . x . . . ) |  2 | 96  *  * |  2  2  1   0  0 |  1  2  0  0  3  0  2 |  1 0 1  3
      s . 2 . s   |  2 |  * 96  * |  0  2  0   4  0 |  0  1  2  0  4  2  0 |  2 1 0  2
      . . . o4s   |  2 |  *  * 96 |  0  0  1   2  2 |  0  0  1  1  2  2  2 |  1 1 1  2
------------------+----+----------+-----------------+----------------------+----------
demi( . x3o . . ) |  3 |  3  0  0 | 64  *  *   *  * |  1  1  0  0  0  0  1 |  0 0 1  2
      s2x . 2 s   |  4 |  2  2  0 |  * 96  *   *  * |  0  1  0  0  2  0  0 |  1 0 0  2
      . x 2 o4s   |  4 |  2  0  2 |  *  * 48   *  * |  0  0  0  0  2  0  2 |  1 0 1  2
sefa( s . 2 o4s ) |  3 |  0  2  1 |  *  *  * 192  * |  0  0  1  0  1  1  0 |  1 1 0  1
sefa( . . o3o4s ) |  3 |  0  0  3 |  *  *  *   * 64 |  0  0  0  1  0  1  1 |  0 1 1  1
------------------+----+----------+-----------------+----------------------+----------
demi( . x3o3o . )   4 |  6  0  0 |  4  0  0   0  0 | 16  *  *  *  *  *  * |  0 0 1  1
      s2x3o 2 s     6 |  6  3  0 |  2  3  0   0  0 |  * 32  *  *  *  *  * |  0 0 0  2
      s . 2 o4s     4 |  0  4  2 |  0  0  0   4  0 |  *  * 48  *  *  *  * |  1 1 0  0
      . . o3o4s     4 |  0  0  6 |  0  0  0   0  4 |  *  *  * 16  *  *  * |  0 1 1  0
sefa( s2x 2 o4s )   6 |  3  4  2 |  0  2  1   2  0 |  *  *  *  * 96  *  * |  1 0 0  1
sefa( s 2 o3o4s )   4 |  0  3  3 |  0  0  0   3  1 |  *  *  *  *  * 64  * |  0 1 0  1
sefa( . x3o3o4s )  12 | 12  0 12 |  4  0  6   0  4 |  *  *  *  *  *  * 16 |  0 0 1  1
------------------+----+----------+-----------------+----------------------+----------
      s2x 2 o4s     8 |  4  8  4 |  0  4  2   8  0 |  0  0  2  0  4  0  0 | 24 * *  *
      s 2 o3o4s     8 |  0 12 12 |  0  0  0  24  8 |  0  0  6  2  0  8  0 |  * 8 *  *
      . x3o3o4s    32 | 48  0 48 | 32  0 24   0 32 |  8  0  0  8  0  0  8 |  * * 2  *
sefa( s2x3o3o4s )  16 | 18 12 12 |  8 12  6  12  4 |  1  4  0  0  6  4  1 |  * * * 16

starting figure: x x3o3o4x

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