Acronym pexhin (old: tutas) Name partially expanded hemipenteract,truncated tetrahedron altersquarism,tuta alterprism,cyclodiminished siphin Circumradius sqrt(13/8) = 1.274755 Lace cityin approx. ASCII-art ```T t -- xo3xx3ox&#x (tuta) t T -- ox3xx3xo&#x (alt. tuta) where: T = x3x3o (tut) t = o3x3x (inv. tut) ``` Confer uniform relative: siphin   related segmentotera: rita   tutaf   general polytopal classes: scaliform   segmentotera   altersquarism   partial Stott expansions Externallinks

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

```xo3xx3ox xo ox&#zx   → height = 0
(tegum sum of 2 base-inverted lacing-ortho tuttips)

o.3o.3o. o. o.     & | 48 |  1  2  1  4 |  2  1  2  6  4  6 | 1 1  6  2  4  6  2 | 2  4 1  2
---------------------+----+-------------+-------------------+--------------------+----------
x. .. .. .. ..     & |  2 | 24  *  *  * |  2  0  0  4  0  0 | 1 0  4  2  2  0  0 | 2  2 1  0
.. x. .. .. ..     & |  2 |  * 48  *  * |  1  1  1  0  2  0 | 1 1  4  0  0  3  0 | 2  3 0  1
.. .. .. x. ..     & |  2 |  *  * 24  * |  0  0  2  0  0  4 | 0 1  0  0  2  4  2 | 0  2 1  2
oo3oo3oo oo oo&#x    |  2 |  *  *  * 96 |  0  0  0  2  1  2 | 0 0  2  1  2  2  1 | 1  2 1  1
---------------------+----+-------------+-------------------+--------------------+----------
x.3x. .. .. ..     & |  6 |  3  3  0  0 | 16  *  *  *  *  * | 1 0  2  0  0  0  0 | 2  1 0  0
.. x.3o. .. ..     & |  3 |  0  3  0  0 |  * 16  *  *  *  * | 1 1  2  0  0  0  0 | 2  2 0  0
.. x. .. x. ..     & |  4 |  0  2  2  0 |  *  * 24  *  *  * | 0 1  0  0  0  2  0 | 0  2 0  1
xo .. .. .. ..&#x  & |  3 |  1  0  0  2 |  *  *  * 96  *  * | 0 0  1  1  1  0  0 | 1  1 1  0
.. xx .. .. ..&#x  & |  4 |  0  2  0  2 |  *  *  *  * 48  * | 0 0  2  0  0  2  0 | 1  2 0  1
.. .. .. xo ..&#x  & |  3 |  0  0  1  2 |  *  *  *  *  * 96 | 0 0  0  0  1  1  1 | 0  1 1  1
---------------------+----+-------------+-------------------+--------------------+----------
x.3x.3o. .. ..     & ♦ 12 |  6 12  0  0 |  4  4  0  0  0  0 | 4 *  *  *  *  *  * | 2  0 0  0
.. x.3o. x. ..     & ♦  6 |  0  6  3  0 |  0  2  3  0  0  0 | * 8  *  *  *  *  * | 0  2 0  0
xo3xx .. .. ..&#x  & ♦  9 |  3  6  0  6 |  1  1  0  3  3  0 | * * 32  *  *  *  * | 1  1 0  0
xo .. ox .. ..&#x    ♦  4 |  2  0  0  4 |  0  0  0  4  0  0 | * *  * 24  *  *  * | 1  0 1  0
xo .. .. .. ox&#x  & ♦  4 |  1  0  1  4 |  0  0  0  2  0  2 | * *  *  * 48  *  * | 0  1 1  0
.. xx .. xo ..&#x  & ♦  6 |  0  3  2  4 |  0  0  1  0  2  2 | * *  *  *  * 48  * | 0  1 0  1
.. .. .. xo ox&#x    ♦  4 |  0  0  2  4 |  0  0  0  0  0  4 | * *  *  *  *  * 24 | 0  0 1  1
---------------------+----+-------------+-------------------+--------------------+----------
xo3xx3ox .. ..&#x    ♦ 24 | 12 24  0 24 |  8  8  0 24 12  0 | 2 0  8  6  0  0  0 | 4  * *  *
xo3xx .. .. ox&#x  & ♦ 12 |  3  9  3 12 |  1  2  3  6  6  6 | 0 1  2  0  3  3  0 | * 16 *  *
xo .. ox xo ox&#zx   ♦  8 |  4  0  4 16 |  0  0  0 16  0 16 | 0 0  0  4  8  0  4 | *  * 6  *
.. xx .. xo ox&#x    ♦  8 |  0  4  4  8 |  0  0  2  0  4  8 | 0 0  0  0  0  4  2 | *  * * 12
```

```xo3xx3ox&#x || ox3xx3xo&#x   → height = 1/sqrt(2) = 0.707107

o.3o.3o.      .. .. ..     & | 48 |  1  2  4  1 |  2  1  6  4  6  2 | 1  6  2  4  6  2 1 | 2  4 1  2
-----------------------------+----+-------------+-------------------+--------------------+----------
x. .. ..      .. .. ..     & |  2 | 24  *  *  * |  2  0  4  0  0  0 | 1  4  2  2  0  0 0 | 2  2 1  0
.. x. ..      .. .. ..     & |  2 |  * 48  *  * |  1  1  0  2  0  1 | 1  4  0  0  3  0 1 | 2  3 0  1
oo3oo3oo&#x   .. .. ..     & |  2 |  *  * 96  * |  0  0  2  1  2  0 | 0  2  1  2  2  1 0 | 1  2 1  1
o.3o.3o.    || .o3.o3.o     & |  2 |  *  *  * 24 |  0  0  0  0  4  2 | 0  0  0  2  4  2 1 | 0  2 1  2
-----------------------------+----+-------------+-------------------+--------------------+----------
x.3x. ..      .. .. ..     & |  6 |  3  3  0  0 | 16  *  *  *  *  * | 1  2  0  0  0  0 0 | 2  1 0  0
.. x.3o.      .. .. ..     & |  3 |  0  3  0  0 |  * 16  *  *  *  * | 1  2  0  0  0  0 1 | 2  2 0  0
xo .. ..&#x   .. .. ..     & |  3 |  1  0  2  0 |  *  * 96  *  *  * | 0  1  1  1  0  0 0 | 1  1 1  0
.. xx ..&#x   .. .. ..     & |  4 |  0  2  2  0 |  *  *  * 48  *  * | 0  2  0  0  2  0 0 | 1  2 0  1
oo3oo3oo&#x || o.3o.3o.     & |  3 |  0  0  2  1 |  *  *  *  * 96  * | 0  0  0  1  1  1 0 | 0  1 1  1
.. x. ..    || .. .x ..     & |  4 |  0  2  0  2 |  *  *  *  *  * 24 | 0  0  0  0  2  0 1 | 0  2 0  1
-----------------------------+----+-------------+-------------------+--------------------+----------
x.3x.3o.      .. .. ..     & ♦ 12 |  6 12  0  0 |  4  4  0  0  0  0 | 4  *  *  *  *  * * | 2  0 0  0
xo3xx ..&#x   .. .. ..     & ♦  9 |  3  6  6  0 |  1  1  3  3  0  0 | * 32  *  *  *  * * | 1  1 0  0
xo .. ox&#x   .. .. ..     & ♦  4 |  2  0  4  0 |  0  0  4  0  0  0 | *  * 24  *  *  * * | 1  0 1  0
xo .. ..&#x || o.3o.3o.     & ♦  4 |  1  0  4  1 |  0  0  2  0  2  0 | *  *  * 48  *  * * | 0  1 1  0
.. xx ..&#x || .. x. ..     & ♦  6 |  0  3  4  2 |  0  0  0  2  2  1 | *  *  *  * 48  * * | 0  1 0  1
oo3oo3oo&#x || oo3oo3oo&#x    ♦  4 |  0  0  4  2 |  0  0  0  0  4  0 | *  *  *  *  * 24 * | 0  0 1  1
.. x.3o.    || .. .x3.o     & ♦  6 |  0  6  0  3 |  0  2  0  0  0  3 | *  *  *  *  *  * 8 | 0  2 0  0
-----------------------------+----+-------------+-------------------+--------------------+----------
xo3xx3ox&#x   .. .. ..     & ♦ 24 | 12 24 24  0 |  8  8 24 12  0  0 | 2  8  6  0  0  0 0 | 4  * *  *
xo3xx ..&#x || o.3x. ..     & ♦ 12 |  3  9 12  3 |  1  2  6  6  6  3 | 0  2  0  3  3  0 1 | * 16 *  *
xo .. ox&#x || ox .. xo&#x    ♦  8 |  4  0 16  4 |  0  0 16  0 16  0 | 0  0  4  8  0  4 0 | *  * 6  *
.. xx ..&#x || .. xx ..&#x    ♦  8 |  0  4  8  4 |  0  0  0  4  8  2 | 0  0  0  0  4  2 0 | *  * * 12
```

```xoxo3xxxx3oxox&#xr   → all cyclical heights = 1/sqrt(2) = 0.707107

o...3o...3o...     & | 48 |  1  2  4  1 |  2  1  6  4  6  2 | 1  6  2  4  6  2 1 | 2  4 1  2
---------------------+----+-------------+-------------------+--------------------+----------
x... .... ....     & |  2 | 24  *  *  * |  2  0  4  0  0  0 | 1  4  2  2  0  0 0 | 2  2 1  0
.... x... ....     & |  2 |  * 48  *  * |  1  1  0  2  0  1 | 1  4  0  0  3  0 1 | 2  3 0  1
oo..3oo..3oo..&#x  & |  2 |  *  * 96  * |  0  0  2  1  2  0 | 0  2  1  2  2  1 0 | 1  2 1  1
o.o.3o.o.3o.o.&#x  & |  2 |  *  *  * 24 |  0  0  0  0  4  2 | 0  0  0  2  4  2 1 | 0  2 1  2
---------------------+----+-------------+-------------------+--------------------+----------
x...3x... ....     & |  6 |  3  3  0  0 | 16  *  *  *  *  * | 1  2  0  0  0  0 0 | 2  1 0  0
.... x...3o...     & |  3 |  0  3  0  0 |  * 16  *  *  *  * | 1  2  0  0  0  0 1 | 2  2 0  0
xo.. .... ....&#x  & |  3 |  1  0  2  0 |  *  * 96  *  *  * | 0  1  1  1  0  0 0 | 1  1 1  0
.... xx.. ....&#x  & |  4 |  0  2  2  0 |  *  *  * 48  *  * | 0  2  0  0  2  0 0 | 1  2 0  1
ooo.3ooo.3ooo.&#x  & |  3 |  0  0  2  1 |  *  *  *  * 96  * | 0  0  0  1  1  1 0 | 0  1 1  1
.... x.x. ....&#x  & |  4 |  0  2  0  2 |  *  *  *  *  * 24 | 0  0  0  0  2  0 1 | 0  2 0  1
---------------------+----+-------------+-------------------+--------------------+----------
x...3x...3o...     & ♦ 12 |  6 12  0  0 |  4  4  0  0  0  0 | 4  *  *  *  *  * * | 2  0 0  0
xo..3xx.. ....&#x  & ♦  9 |  3  6  6  0 |  1  1  3  3  0  0 | * 32  *  *  *  * * | 1  1 0  0
xo.. .... ox..&#x  & ♦  4 |  2  0  4  0 |  0  0  4  0  0  0 | *  * 24  *  *  * * | 1  0 1  0
xo.o .... ....&#x  & ♦  4 |  1  0  4  1 |  0  0  2  0  2  0 | *  *  * 48  *  * * | 0  1 1  0
.... xxx. ....&#x  & ♦  6 |  0  3  4  2 |  0  0  0  2  2  1 | *  *  *  * 48  * * | 0  1 0  1
oooo3oooo3oooo&#x    ♦  4 |  0  0  4  2 |  0  0  0  0  4  0 | *  *  *  *  * 24 * | 0  0 1  1
.... x.x.3o.o.&#x  & ♦  6 |  0  6  0  3 |  0  2  0  0  0  3 | *  *  *  *  *  * 8 | 0  2 0  0
---------------------+----+-------------+-------------------+--------------------+----------
xo..3xx..3ox..&#x  & ♦ 24 | 12 24 24  0 |  8  8 24 12  0  0 | 2  8  6  0  0  0 0 | 4  * *  *
xo.o3xx.x ....&#x  & ♦ 12 |  3  9 12  3 |  1  2  6  6  6  3 | 0  2  0  3  3  0 1 | * 16 *  *
xoxo .... oxox&#xr   ♦  8 |  4  0 16  4 |  0  0 16  0 16  0 | 0  0  4  8  0  4 0 | *  * 6  *
.... xxxx ....&#x    ♦  8 |  0  4  8  4 |  0  0  0  4  8  2 | 0  0  0  0  4  2 0 | *  * * 12
```