﻿ traffip
 Acronym traffip Name traf prism,trip atop inverted tisdip Circumradius sqrt(17/20) = 0.921954 Lace cityin approx. ASCII-art ``` x x3o x o3x x o3x ``` Confer uniform relative: rappip   general polytopal classes: segmentotera   lace simplices

Incidence matrix according to Dynkin symbol

```ox xx ox3xo&#x   → height = sqrt(5/12) = 0.645497
(trip || inv tisdip)

o. o. o.3o.    | 6  * | 1 2  4 0 0  0 | 2 1  2  4  2  4 0 0 0 0 | 1 2 1 2 2 4 2 0 0 0 | 1 2 1 2 0
.o .o .o3.o    | * 12 | 0 0  2 1 1  2 | 0 0  2  2  2  1 1 2 2 1 | 0 2 2 1 2 1 1 2 1 1 | 2 1 1 1 1
---------------+------+---------------+-------------------------+---------------------+----------
.. x. .. ..    | 2  0 | 3 *  * * *  * | 2 0  0  4  0  0 0 0 0 0 | 1 2 0 0 2 4 0 0 0 0 | 1 2 0 2 0
.. .. .. x.    | 2  0 | * 6  * * *  * | 1 1  0  0  0  2 0 0 0 0 | 1 0 0 1 0 2 2 0 0 0 | 0 1 1 2 0
oo oo oo3oo&#x | 1  1 | * * 24 * *  * | 0 0  1  1  1  1 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
.x .. .. ..    | 0  2 | * *  * 6 *  * | 0 0  2  0  0  0 1 2 0 0 | 0 2 2 1 0 0 0 2 1 0 | 2 1 1 0 1
.. .x .. ..    | 0  2 | * *  * * 6  * | 0 0  0  2  0  0 1 0 2 0 | 0 2 0 0 2 1 0 2 0 1 | 2 1 0 1 1
.. .. .x ..    | 0  2 | * *  * * * 12 | 0 0  0  0  1  0 0 1 1 1 | 0 0 1 0 1 0 1 1 1 1 | 1 0 1 1 1
---------------+------+---------------+-------------------------+---------------------+----------
.. x. .. x.    | 4  0 | 2 2  0 0 0  0 | 3 *  *  *  *  * * * * * | 1 0 0 0 0 2 0 0 0 0 | 0 1 0 2 0
.. .. o.3x.    | 3  0 | 0 3  0 0 0  0 | * 2  *  *  *  * * * * * | 1 0 0 0 0 0 2 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x | 1  2 | 0 0  2 1 0  0 | * * 12  *  *  * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
.. xx .. ..&#x | 2  2 | 1 0  2 0 1  0 | * *  * 12  *  * * * * * | 0 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0
.. .. ox ..&#x | 1  2 | 0 0  2 0 0  1 | * *  *  * 12  * * * * * | 0 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0
.. .. .. xo&#x | 2  1 | 0 1  2 0 0  0 | * *  *  *  * 12 * * * * | 0 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0
.x .x .. ..    | 0  4 | 0 0  0 2 2  0 | * *  *  *  *  * 3 * * * | 0 2 0 0 0 0 0 2 0 0 | 2 1 0 0 1
.x .. .x ..    | 0  4 | 0 0  0 2 0  2 | * *  *  *  *  * * 6 * * | 0 0 1 0 0 0 0 1 1 0 | 1 0 1 0 1
.. .x .x ..    | 0  4 | 0 0  0 0 2  2 | * *  *  *  *  * * * 6 * | 0 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1
.. .. .x3.o    | 0  3 | 0 0  0 0 0  3 | * *  *  *  *  * * * * 4 | 0 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
---------------+------+---------------+-------------------------+---------------------+----------
.. x. o.3x.    ♦ 6  0 | 3 6  0 0 0  0 | 3 2  0  0  0  0 0 0 0 0 | 1 * * * * * * * * * | 0 0 0 2 0
ox xx .. ..&#x ♦ 2  4 | 1 0  4 2 2  0 | 0 0  2  2  0  0 1 0 0 0 | * 6 * * * * * * * * | 1 1 0 0 0
ox .. ox ..&#x ♦ 1  4 | 0 0  4 2 0  2 | 0 0  2  0  2  0 0 1 0 0 | * * 6 * * * * * * * | 1 0 1 0 0
ox .. .. xo&#x ♦ 2  2 | 0 1  4 1 0  0 | 0 0  2  0  0  2 0 0 0 0 | * * * 6 * * * * * * | 0 1 1 0 0
.. xx ox ..&#x ♦ 2  4 | 1 0  4 0 2  2 | 0 0  0  2  2  0 0 0 1 0 | * * * * 6 * * * * * | 1 0 0 1 0
.. xx .. xo&#x ♦ 4  2 | 2 2  4 0 1  0 | 1 0  0  2  0  2 0 0 0 0 | * * * * * 6 * * * * | 0 1 0 1 0
.. .. ox3xo&#x ♦ 3  3 | 0 3  6 0 0  3 | 0 1  0  0  3  3 0 0 0 1 | * * * * * * 4 * * * | 0 0 1 1 0
.x .x .x ..    ♦ 0  8 | 0 0  0 4 4  4 | 0 0  0  0  0  0 2 2 2 0 | * * * * * * * 3 * * | 1 0 0 0 1
.x .. .x3.o    ♦ 0  6 | 0 0  0 3 0  6 | 0 0  0  0  0  0 0 3 0 2 | * * * * * * * * 2 * | 0 0 1 0 1
.. .x .x3.o    ♦ 0  6 | 0 0  0 0 3  6 | 0 0  0  0  0  0 0 0 3 2 | * * * * * * * * * 2 | 0 0 0 1 1
---------------+------+---------------+-------------------------+---------------------+----------
ox xx ox ..&#x ♦ 2  8 | 1 0  8 4 4  4 | 0 0  4  4  4  0 2 2 2 0 | 0 2 2 0 2 0 0 1 0 0 | 3 * * * *
ox xx .. xo&#x ♦ 4  4 | 2 2  8 2 2  0 | 1 0  4  4  0  4 1 0 0 0 | 0 2 0 2 0 2 0 0 0 0 | * 3 * * *
ox .. ox3xo&#x ♦ 3  6 | 0 3 12 3 0  6 | 0 1  6  0  6  6 0 3 0 2 | 0 0 3 3 0 0 2 0 1 0 | * * 2 * *
.. xx ox3xo&#x ♦ 6  6 | 3 6 12 0 3  6 | 3 2  0  6  6  6 0 0 3 2 | 1 0 0 0 3 3 2 0 0 1 | * * * 2 *
.x .x .x3.o    ♦ 0 12 | 0 0  0 6 6 12 | 0 0  0  0  0  0 3 6 6 4 | 0 0 0 0 0 0 0 3 2 2 | * * * * 1
```

```xxx oox3xxo&#x   → height(1,2) = 1
height(1,3) = height(2,3) = sqrt(2/3) = 0.816497

o.. o..3o..    | 6 * * | 1 2 1  2 0 0  0 0 0 | 2 1 1 2  2 2 1 2 0 0 0 0 0 0 0 | 1 2 1 2 1 2 1 2 1 0 0 0 0 0 | 1 1 2 1 1 0
.o. .o.3.o.    | * 6 * | 0 0 1  0 1 2  2 0 0 | 0 0 1 2  2 0 0 0 2 1 2 1 2 0 0 | 0 2 1 2 1 2 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o ..o3..o    | * * 6 | 0 0 0  2 0 0  2 1 2 | 0 0 0 0  2 2 2 1 0 0 2 2 1 2 1 | 0 0 0 2 2 1 2 1 1 0 2 1 1 1 | 0 2 1 1 1 1
---------------+-------+---------------------+--------------------------------+-----------------------------+------------
x.. ... ...    | 2 0 0 | 3 * *  * * *  * * * | 2 0 1 0  0 2 0 0 0 0 0 0 0 0 0 | 1 2 0 2 0 0 1 2 0 0 0 0 0 0 | 1 1 2 0 0 0
... ... x..    | 2 0 0 | * 6 *  * * *  * * * | 1 1 0 1  0 0 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 1 0
oo. oo.3oo.&#x | 1 1 0 | * * 6  * * *  * * * | 0 0 1 2  2 0 0 0 0 0 0 0 0 0 0 | 0 2 1 2 1 2 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o o.o3o.o&#x | 1 0 1 | * * * 12 * *  * * * | 0 0 0 0  1 1 1 1 0 0 0 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x. ... ...    | 0 2 0 | * * *  * 3 *  * * * | 0 0 1 0  0 0 0 0 2 0 2 0 0 0 0 | 0 2 0 2 0 0 0 0 0 1 1 2 0 0 | 1 1 2 0 0 1
... ... .x.    | 0 2 0 | * * *  * * 6  * * * | 0 0 0 1  0 0 0 0 1 1 0 0 1 0 0 | 0 1 1 0 0 1 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo .oo3.oo&#x | 0 1 1 | * * *  * * * 12 * * | 0 0 0 0  1 0 0 0 0 0 1 1 1 0 0 | 0 0 0 1 1 1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    | 0 0 2 | * * *  * * *  * 3 * | 0 0 0 0  0 2 0 0 0 0 2 0 0 2 0 | 0 0 0 2 0 0 2 1 0 0 2 1 0 1 | 0 2 1 0 1 1
... ..x ...    | 0 0 2 | * * *  * * *  * * 6 | 0 0 0 0  0 0 1 0 0 0 0 1 0 1 1 | 0 0 0 0 1 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
---------------+-------+---------------------+--------------------------------+-----------------------------+------------
x.. ... x..    | 4 0 0 | 2 2 0  0 0 0  0 0 0 | 3 * * *  * * * * * * * * * * * | 1 1 0 0 0 0 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
... o..3x..    | 3 0 0 | 0 3 0  0 0 0  0 0 0 | * 2 * *  * * * * * * * * * * * | 1 0 1 0 0 0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
xx. ... ...&#x | 2 2 0 | 1 0 2  0 1 0  0 0 0 | * * 3 *  * * * * * * * * * * * | 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
... ... xx.&#x | 2 2 0 | 0 1 2  0 0 1  0 0 0 | * * * 6  * * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo ooo3ooo&#x | 1 1 1 | 0 0 1  1 0 0  1 0 0 | * * * * 12 * * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
x.x ... ...&#x | 2 0 2 | 1 0 0  2 0 0  0 1 0 | * * * *  * 6 * * * * * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... o.x ...&#x | 1 0 2 | 0 0 0  2 0 0  0 0 1 | * * * *  * * 6 * * * * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.o&#x | 2 0 1 | 0 1 0  2 0 0  0 0 0 | * * * *  * * * 6 * * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x. ... .x.    | 0 4 0 | 0 0 0  0 2 2  0 0 0 | * * * *  * * * * 3 * * * * * * | 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .o.3.x.    | 0 3 0 | 0 0 0  0 0 3  0 0 0 | * * * *  * * * * * 2 * * * * * | 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x | 0 2 2 | 0 0 0  0 1 0  2 1 0 | * * * *  * * * * * * 6 * * * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .ox ...&#x | 0 1 2 | 0 0 0  0 0 0  2 0 1 | * * * *  * * * * * * * 6 * * * | 0 0 0 0 1 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xo&#x | 0 2 1 | 0 0 0  0 0 1  2 0 0 | * * * *  * * * * * * * * 6 * * | 0 0 0 0 0 1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x ..x ...    | 0 0 4 | 0 0 0  0 0 0  0 2 2 | * * * *  * * * * * * * * * 3 * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
... ..x3..o    | 0 0 3 | 0 0 0  0 0 0  0 0 3 | * * * *  * * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+-------+---------------------+--------------------------------+-----------------------------+------------
x.. o..3x..    ♦ 6 0 0 | 3 6 0  0 0 0  0 0 0 | 3 2 0 0  0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 0 0 0 1 0
xx. ... xx.&#x ♦ 4 4 0 | 2 2 4  0 2 2  0 0 0 | 1 0 2 2  0 0 0 0 1 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * | 1 0 1 0 0 0
... oo.3xx.&#x ♦ 3 3 0 | 0 3 3  0 0 3  0 0 0 | 0 1 0 3  0 0 0 0 0 1 0 0 0 0 0 | * * 2 * * * * * * * * * * * | 1 0 0 1 0 0
xxx ... ...&#x ♦ 2 2 2 | 1 0 2  2 1 0  2 1 0 | 0 0 1 0  2 1 0 0 0 0 1 0 0 0 0 | * * * 6 * * * * * * * * * * | 0 1 1 0 0 0
... oox ...&#x ♦ 1 1 2 | 0 0 1  2 0 0  2 0 1 | 0 0 0 0  2 0 1 0 0 0 0 1 0 0 0 | * * * * 6 * * * * * * * * * | 0 1 0 1 0 0
... ... xxo&#x ♦ 2 2 1 | 0 1 2  2 0 1  2 0 0 | 0 0 0 1  2 0 0 1 0 0 0 0 1 0 0 | * * * * * 6 * * * * * * * * | 0 0 1 1 0 0
x.x o.x ...&#x ♦ 2 0 4 | 1 0 0  4 0 0  0 2 2 | 0 0 0 0  0 2 2 0 0 0 0 0 0 1 0 | * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
x.x ... x.o&#x ♦ 4 0 2 | 2 2 0  4 0 0  0 1 0 | 1 0 0 0  0 2 0 2 0 0 0 0 0 0 0 | * * * * * * * 3 * * * * * * | 0 0 1 0 1 0
... o.x3x.o&#x ♦ 3 0 3 | 0 3 0  6 0 0  0 0 3 | 0 1 0 0  0 0 3 3 0 0 0 0 0 0 1 | * * * * * * * * 2 * * * * * | 0 0 0 1 1 0
.x. .o.3.x.    ♦ 0 6 0 | 0 0 0  0 3 6  0 0 0 | 0 0 0 0  0 0 0 0 3 2 0 0 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xx .ox ...&#x ♦ 0 2 4 | 0 0 0  0 1 0  4 2 2 | 0 0 0 0  0 0 0 0 0 0 2 2 0 1 0 | * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.xx ... .xo&#x ♦ 0 4 2 | 0 0 0  0 2 2  4 1 0 | 0 0 0 0  0 0 0 0 1 0 2 0 2 0 0 | * * * * * * * * * * * 3 * * | 0 0 1 0 0 1
... .ox3.xo&#x | 0 3 3 | 0 0 0  0 0 3  6 0 3 | 0 0 0 0  0 0 0 0 0 1 0 3 3 0 1 | * * * * * * * * * * * * 2 * | 0 0 0 1 0 1 oct
..x ..x3..o    ♦ 0 0 6 | 0 0 0  0 0 0  0 3 6 | 0 0 0 0  0 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------+-------+---------------------+--------------------------------+-----------------------------+------------
xx. oo.3xx.&#x ♦ 6 6 0 | 3 6 6  0 3 6  0 0 0 | 3 2 3 6  0 0 0 0 3 2 0 0 0 0 0 | 1 3 2 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * *
xxx oox ...&#x ♦ 2 2 4 | 1 0 2  4 1 0  4 2 2 | 0 0 1 0  4 2 2 0 0 0 2 2 0 1 0 | 0 0 0 2 2 0 1 0 0 0 1 0 0 0 | * 3 * * * *
xxx ... xxo&#x ♦ 4 4 2 | 2 2 4  4 2 2  4 1 0 | 1 0 2 2  4 2 0 2 1 0 2 0 2 0 0 | 0 1 0 2 0 2 0 1 0 0 0 1 0 0 | * * 3 * * *
... oox3xxo&#x ♦ 3 3 3 | 0 3 3  6 0 3  6 0 3 | 0 1 0 3  6 0 3 3 0 1 0 3 3 0 1 | 0 0 1 0 3 3 0 0 1 0 0 0 1 0 | * * * 2 * *
x.x o.x3x.o&#x ♦ 6 0 6 | 3 6 0 12 0 0  0 3 6 | 3 2 0 0  0 6 6 6 0 0 0 0 0 3 2 | 1 0 0 0 0 0 3 3 2 0 0 0 0 1 | * * * * 1 *
.xx .ox3.xo&#x ♦ 0 6 6 | 0 0 0  0 3 6 12 3 6 | 0 0 0 0  0 0 0 0 3 2 6 6 6 3 2 | 0 0 0 0 0 0 0 0 0 1 3 3 2 1 | * * * * * 1
```

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