| Acronym | pexhin (old: tutas) |
| Name |
partially expanded hemipenteract, truncated tetrahedron altersquarism, tuta alterprism, cyclodiminished siphin |
| Circumradius | sqrt(13/8) = 1.274755 |
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Lace city in approx. ASCII-art |
T t -- xo3xx3ox&#x (tuta) t T -- ox3xx3xo&#x (alt. tuta) where: T = x3x3o (tut) t = o3x3x (inv. tut) |
| Face vector | 48, 192, 296, 188, 38 |
| Confer |
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External links |
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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
s4o2x3o4s
demi( . . . . . ) | 48 | 2 1 4 1 | 1 2 4 6 6 2 | 1 2 2 1 6 4 6 | 2 1 2 4
------------------+----+-------------+-------------------+--------------------+----------
demi( . . x . . ) | 2 | 48 * * * | 1 1 2 0 0 1 | 1 0 0 1 3 0 4 | 1 0 2 3
s4o . . . | 2 | * 24 * * | 0 2 0 4 0 0 | 1 2 0 0 4 2 0 | 2 1 0 2
s . 2 . s | 2 | * * 96 * | 0 0 1 2 2 0 | 0 1 1 0 2 2 2 | 1 1 1 2
. . . o4s | 2 | * * * 24 | 0 0 0 0 4 2 | 0 0 2 1 0 2 4 | 0 1 2 2
------------------+----+-------------+-------------------+--------------------+----------
demi( . . x3o . ) | 3 | 3 0 0 0 | 16 * * * * * | 1 0 0 1 0 0 2 | 0 0 2 2
s4o2x . . | 4 | 2 2 0 0 | * 24 * * * * | 1 0 0 0 2 0 0 | 1 0 0 2
s 2 x 2 s | 4 | 2 0 2 0 | * * 48 * * * | 0 0 0 0 2 0 2 | 1 0 1 2
sefa( s4o 2 . s ) | 3 | 0 1 2 0 | * * * 96 * * | 0 1 0 0 1 1 0 | 1 1 0 1
sefa( s . 2 o4s ) | 3 | 0 0 2 1 | * * * * 96 * | 0 0 1 0 0 1 1 | 0 1 1 1
sefa( . . x3o4s ) | 6 | 3 0 0 3 | * * * * * 16 | 0 0 0 1 0 0 2 | 0 0 2 1
------------------+----+-------------+-------------------+--------------------+----------
s4o2x3o . ♦ 6 | 6 3 0 0 | 2 3 0 0 0 0 | 8 * * * * * * | 0 0 0 2
s4o 2 . s ♦ 4 | 0 2 4 0 | 0 0 0 4 0 0 | * 24 * * * * * | 1 1 0 0
s . 2 o4s ♦ 4 | 0 0 4 2 | 0 0 0 0 4 0 | * * 24 * * * * | 0 1 1 0
. . x3o4s ♦ 12 | 12 0 0 6 | 4 0 0 0 0 4 | * * * 4 * * * | 0 0 2 0
sefa( s4o2x 2 s ) ♦ 6 | 3 2 4 0 | 0 1 2 2 0 0 | * * * * 48 * * | 1 0 0 1
sefa( s4o 2 o4s ) ♦ 4 | 0 1 4 1 | 0 0 0 2 2 0 | * * * * * 48 * | 0 1 0 1
sefa( s 2 x3o4s ) ♦ 9 | 6 0 6 3 | 1 0 3 0 3 1 | * * * * * * 32 | 0 0 1 1
------------------+----+-------------+-------------------+--------------------+----------
s4o2x 2 s ♦ 8 | 4 4 8 0 | 0 2 4 8 0 0 | 0 2 0 0 4 0 0 | 12 * * *
s4o 2 o4s ♦ 8 | 0 4 16 4 | 0 0 0 16 16 0 | 0 4 4 0 0 8 0 | * 6 * *
s 2 x3o4s ♦ 24 | 24 0 24 12 | 8 0 12 0 24 8 | 0 0 6 2 0 0 8 | * * 4 *
sefa( s4o2x3o4s ) ♦ 12 | 9 3 12 3 | 2 3 6 6 6 1 | 1 0 0 0 3 3 2 | * * * 16
starting figure: x4o x3o4x
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
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