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
Face vector	64, 288, 464, 288, 50
Confer	uniform relative: siphin general polytopal classes: scaliform   segmentotera   lace simplices
External links

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