﻿ trafpy
 Acronym trafpy Name triangular antifastegium pyramid,(triangular prism, gyro triangular pyramid)-disphenoid Circumradius sqrt(5/8) = 0.790569 Lace cityin approx. ASCII-art ```o 3 P where: o = o o3o (point) 3 = o o3x (triangle) P = x x3o (gyrated trip) ``` Lace hyper cityin approx. ASCII-art ```x3o x3o o3x o3o ``` (disphenoid in configuration space) Confer uniform relative: hin   related segmentotera: rappy   general polytopal classes: segmentotera   lace simplices

Incidence matrix according to Dynkin symbol

```oox oox3oxo&#x   → height(1,2) = sqrt(2/3) = 0.816497
height(1,3) = height(2,3) = sqrt(5/12) = 0.645497

o.. o..3o..    | 1 * * ♦ 3 6 0  0 0 0 | 3 3 6 12 0 0 0 0 0 0 | 1 3 2 6 6 6 0 0 0 0 | 1 3 3 2 0
.o. .o.3.o.    | * 3 * | 1 0 2  4 0 0 | 2 0 0  4 1 2 2 4 0 0 | 1 0 0 2 2 4 1 2 2 0 | 0 1 2 2 1
..o ..o3..o    | * * 6 | 0 1 0  2 1 2 | 0 1 2  2 0 2 2 1 2 1 | 0 2 1 2 2 1 2 1 1 1 | 1 2 1 1 1
---------------+-------+--------------+----------------------+---------------------+----------
oo. oo.3oo.&#x | 1 1 0 | 3 * *  * * * | 2 0 0  4 0 0 0 0 0 0 | 1 0 0 2 2 4 0 0 0 0 | 0 1 2 2 0
o.o o.o3o.o&#x | 1 0 1 | * 6 *  * * * | 0 1 2  2 0 0 0 0 0 0 | 0 2 1 2 2 1 0 0 0 0 | 1 2 1 1 0
... ... .x.    | 0 2 0 | * * 3  * * * | 1 0 0  0 1 0 0 2 0 0 | 1 0 0 0 0 2 0 1 2 0 | 0 0 1 2 1
.oo .oo3.oo&#x | 0 1 1 | * * * 12 * * | 0 0 0  1 0 1 1 1 0 0 | 0 0 0 1 1 1 1 1 1 0 | 0 1 1 1 1
..x ... ...    | 0 0 2 | * * *  * 3 * | 0 1 0  0 0 2 0 0 2 0 | 0 2 0 2 0 0 2 1 0 1 | 1 2 1 0 1
... ..x ...    | 0 0 2 | * * *  * * 6 | 0 0 1  0 0 0 1 0 1 1 | 0 1 1 0 1 0 1 0 1 1 | 1 1 0 1 1
---------------+-------+--------------+----------------------+---------------------+----------
... ... ox.&#x | 1 2 0 | 2 0 1  0 0 0 | 3 * *  * * * * * * * | 1 0 0 0 0 2 0 0 0 0 | 0 0 1 2 0
o.x ... ...&#x | 1 0 2 | 0 2 0  0 1 0 | * 3 *  * * * * * * * | 0 2 0 2 0 0 0 0 0 0 | 1 2 1 0 0
... o.x ...&#x | 1 0 2 | 0 2 0  0 0 1 | * * 6  * * * * * * * | 0 1 1 0 1 0 0 0 0 0 | 1 1 0 1 0
ooo ooo3ooo&#x | 1 1 1 | 1 1 0  1 0 0 | * * * 12 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
... .o.3.x.    | 0 3 0 | 0 0 3  0 0 0 | * * *  * 1 * * * * * | 1 0 0 0 0 0 0 0 2 0 | 0 0 0 2 1
.ox ... ...&#x | 0 1 2 | 0 0 0  2 1 0 | * * *  * * 6 * * * * | 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 1
... .ox ...&#x | 0 1 2 | 0 0 0  2 0 1 | * * *  * * * 6 * * * | 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1
... ... .xo&#x | 0 2 1 | 0 0 1  2 0 0 | * * *  * * * * 6 * * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
..x ..x ...    | 0 0 4 | 0 0 0  0 2 2 | * * *  * * * * * 3 * | 0 1 0 0 0 0 1 0 0 1 | 1 1 0 0 1
... ..x3..o    | 0 0 3 | 0 0 0  0 0 3 | * * *  * * * * * * 2 | 0 0 1 0 0 0 0 0 1 1 | 1 0 0 1 1
---------------+-------+--------------+----------------------+---------------------+----------
... oo.3ox.&#x ♦ 1 3 0 | 3 0 3  0 0 0 | 3 0 0  0 1 0 0 0 0 0 | 1 * * * * * * * * * | 0 0 0 2 0
o.x o.x ...&#x ♦ 1 0 4 | 0 4 0  0 2 2 | 0 2 2  0 0 0 0 0 1 0 | * 3 * * * * * * * * | 1 1 0 0 0
... o.x3o.o&#x ♦ 1 0 3 | 0 3 0  0 0 3 | 0 0 3  0 0 0 0 0 0 1 | * * 2 * * * * * * * | 1 0 0 1 0
oox ... ...&#x ♦ 1 1 2 | 1 2 0  2 1 0 | 0 1 0  2 0 1 0 0 0 0 | * * * 6 * * * * * * | 0 1 1 0 0
... oox ...&#x ♦ 1 1 2 | 1 2 0  2 0 1 | 0 0 1  2 0 0 1 0 0 0 | * * * * 6 * * * * * | 0 1 0 1 0
... ... oxo&#x ♦ 1 2 1 | 2 1 1  2 0 0 | 1 0 0  2 0 0 0 1 0 0 | * * * * * 6 * * * * | 0 0 1 1 0
.ox .ox ...&#x ♦ 0 1 4 | 0 0 0  4 2 2 | 0 0 0  0 0 2 2 0 1 0 | * * * * * * 3 * * * | 0 1 0 0 1
.ox ... .xo&#x ♦ 0 2 2 | 0 0 1  4 1 0 | 0 0 0  0 0 2 0 2 0 0 | * * * * * * * 3 * * | 0 0 1 0 1
... .ox3.xo&#x ♦ 0 3 3 | 0 0 3  6 0 3 | 0 0 0  0 1 0 3 3 0 1 | * * * * * * * * 2 * | 0 0 0 1 1
..x ..x3..o    ♦ 0 0 6 | 0 0 0  0 3 6 | 0 0 0  0 0 0 0 0 3 2 | * * * * * * * * * 1 | 1 0 0 0 1
---------------+-------+--------------+----------------------+---------------------+----------
o.x o.x3o.o&#x ♦ 1 0 6 | 0 6 0  0 3 6 | 0 3 6  0 0 0 0 0 3 2 | 0 3 2 0 0 0 0 0 0 1 | 1 * * * *
oox oox ...&#x ♦ 1 1 4 | 1 4 0  4 2 2 | 0 2 2  4 0 2 2 0 1 0 | 0 1 0 2 2 0 1 0 0 0 | * 3 * * *
oox ... oxo&#x ♦ 1 2 2 | 2 2 1  4 1 0 | 1 1 0  4 0 2 0 2 0 0 | 0 0 0 2 0 2 0 1 0 0 | * * 3 * *
... oox3oxo&#x ♦ 1 3 3 | 3 3 3  6 0 3 | 3 0 3  6 1 0 3 3 0 1 | 1 0 1 0 3 3 0 0 1 0 | * * * 2 *
.ox .ox3.xo&#x ♦ 0 3 6 | 0 0 3 12 3 6 | 0 0 0  0 1 6 6 6 3 2 | 0 0 0 0 0 0 3 3 2 1 | * * * * 1
```

```ooox3oxxo&#x   → height(1,2) = height(1,3) = height(1,4) = height(2,4) = height(3,4) = sqrt(2/3) = 1/sqrt(3) = 0.577350
height(2,3) = 1

o...3o...    | 1 * * * ♦ 3 3 3 0 0 0 0 0 0 | 3 3 6 3 6 3 0 0 0 0 0 0 0 0 0 | 1 3 6 3 3 1 3 3 1 0 0 0 0 0 | 1 3 3 1 1 0
.o..3.o..    | * 3 * * | 1 0 0 2 1 2 0 0 0 | 2 1 2 0 0 0 1 2 2 1 2 0 0 0 0 | 1 2 2 1 2 0 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o.3..o.    | * * 3 * | 0 1 0 0 1 0 2 2 0 | 0 1 0 2 2 0 0 2 2 0 0 1 1 2 0 | 0 2 2 0 0 1 1 2 0 1 1 2 0 1 | 1 1 2 0 1 1
...o3...o    | * * * 3 | 0 0 1 0 0 2 0 2 2 | 0 0 2 0 2 2 0 0 2 2 1 0 2 1 1 | 0 0 2 2 1 0 2 1 1 0 2 1 1 1 | 0 2 1 1 1 1
-------------+---------+-------------------+-------------------------------+-----------------------------+------------
oo..3oo..&#x | 1 1 0 0 | 3 * * * * * * * * | 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o.3o.o.&#x | 1 0 1 0 | * 3 * * * * * * * | 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 | 0 2 2 0 0 1 1 2 0 0 0 0 0 0 | 1 1 2 0 1 0
o..o3o..o&#x | 1 0 0 1 | * * 3 * * * * * * | 0 0 2 0 2 2 0 0 0 0 0 0 0 0 0 | 0 0 2 2 1 0 2 1 1 0 0 0 0 0 | 0 2 1 1 1 0
.... .x..    | 0 2 0 0 | * * * 3 * * * * * | 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 | 1 1 0 0 1 0 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo.3.oo.&#x | 0 1 1 0 | * * * * 3 * * * * | 0 1 0 0 0 0 0 2 2 0 0 0 0 0 0 | 0 2 2 0 0 0 0 0 0 1 1 2 0 0 | 1 1 2 0 0 1
.o.o3.o.o&#x | 0 1 0 1 | * * * * * 6 * * * | 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 1 1 1 0 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
.... ..x.    | 0 0 2 0 | * * * * * * 3 * * | 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 | 0 1 0 0 0 1 0 1 0 1 0 1 0 1 | 1 0 1 0 1 1
..oo3..oo&#x | 0 0 1 1 | * * * * * * * 6 * | 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 | 0 0 1 0 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
...x ....    | 0 0 0 2 | * * * * * * * * 3 | 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 | 0 0 0 1 0 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
-------------+---------+-------------------+-------------------------------+-----------------------------+------------
.... ox..&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 0 | 3 * * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo.3ooo.&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | * 3 * * * * * * * * * * * * * | 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 1 0 1 0 0 1 0 0 0 | * * 6 * * * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
.... o.x.&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 0 | * * * 3 * * * * * * * * * * * | 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
o.oo3o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 | * * * * 6 * * * * * * * * * * | 0 0 1 0 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
o..x ....&#x | 1 0 0 2 | 0 0 2 0 0 0 0 0 1 | * * * * * 3 * * * * * * * * * | 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
.o..3.x..    | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 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 2 0 1 0 0 | * * * * * * * 3 * * * * * * * | 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 | * * * * * * * * 6 * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.o.x ....&#x | 0 1 0 2 | 0 0 0 0 0 2 0 0 1 | * * * * * * * * * 3 * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
.... .x.o&#x | 0 2 0 1 | 0 0 0 1 0 2 0 0 0 | * * * * * * * * * * 3 * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..o.3..x.    | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * * 1 * * * | 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1
..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
.... ..xo&#x | 0 0 2 1 | 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
...x3...o    | 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
-------------+---------+-------------------+-------------------------------+-----------------------------+------------
oo..3ox..&#x ♦ 1 3 0 0 | 3 0 0 3 0 0 0 0 0 | 3 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 0 0 1 0 0
.... oxx.&#x ♦ 1 2 2 0 | 2 2 0 1 2 0 1 0 0 | 1 2 0 1 0 0 0 1 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * | 1 0 1 0 0 0
oooo3oooo&#x ♦ 1 1 1 1 | 1 1 1 0 1 1 0 1 0 | 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * | 0 1 1 0 0 0
oo.x ....&#x ♦ 1 1 0 2 | 1 0 2 0 0 2 0 0 1 | 0 0 2 0 0 1 0 0 0 1 0 0 0 0 0 | * * * 3 * * * * * * * * * * | 0 1 0 1 0 0
.... ox.o&#x ♦ 1 2 0 1 | 2 0 1 1 0 2 0 0 0 | 1 0 2 0 0 0 0 0 0 0 1 0 0 0 0 | * * * * 3 * * * * * * * * * | 0 0 1 1 0 0
o.o.3o.x.&#x ♦ 1 0 3 0 | 0 3 0 0 0 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 0 1 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
o.ox ....&#x ♦ 1 0 1 2 | 0 1 2 0 0 0 0 2 1 | 0 0 0 0 2 1 0 0 0 0 0 0 1 0 0 | * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
.... o.xo&#x ♦ 1 0 2 1 | 0 2 1 0 0 0 1 2 0 | 0 0 0 1 2 0 0 0 0 0 0 0 0 1 0 | * * * * * * * 3 * * * * * * | 0 0 1 0 1 0
o..x3o..o&#x ♦ 1 0 0 3 | 0 0 3 0 0 0 0 0 3 | 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 | * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
.oo.3.xx.&#x ♦ 0 3 3 0 | 0 0 0 3 3 0 3 0 0 | 0 0 0 0 0 0 1 3 0 0 0 1 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.oox ....&#x ♦ 0 1 1 2 | 0 0 0 0 1 2 0 2 1 | 0 0 0 0 0 0 0 0 2 1 0 0 1 0 0 | * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.... .xxo&#x ♦ 0 2 2 1 | 0 0 0 1 2 2 1 2 0 | 0 0 0 0 0 0 0 1 2 0 1 0 0 1 0 | * * * * * * * * * * * 3 * * | 0 0 1 0 0 1
.o.x3.x.o&#x ♦ 0 3 0 3 | 0 0 0 3 0 6 0 0 3 | 0 0 0 0 0 0 1 0 0 3 3 0 0 0 1 | * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..ox3..xo&#x ♦ 0 0 3 3 | 0 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+-------------------+-------------------------------+-----------------------------+------------
ooo.3oxx.&#x ♦ 1 3 3 0 | 3 3 0 3 3 0 3 0 0 | 3 3 0 3 0 0 1 3 0 0 0 1 0 0 0 | 1 3 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
ooox ....&#x ♦ 1 1 1 2 | 1 1 2 0 1 2 0 2 1 | 0 1 2 0 2 1 0 0 2 1 0 0 1 0 0 | 0 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 3 * * * *
.... oxxo&#x ♦ 1 2 2 1 | 2 2 1 1 2 2 1 2 0 | 1 2 2 1 2 0 0 1 2 0 1 0 0 1 0 | 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 3 * * *
oo.x3ox.o&#x ♦ 1 3 0 3 | 3 0 3 3 0 6 0 0 3 | 3 0 6 0 0 3 1 0 0 3 3 0 0 0 1 | 1 0 0 3 3 0 0 0 1 0 0 0 1 0 | * * * 1 * *
o.ox3o.xo&#x ♦ 1 0 3 3 | 0 3 3 0 0 0 3 6 3 | 0 0 0 3 6 3 0 0 0 0 0 1 3 3 1 | 0 0 0 0 0 1 3 3 1 0 0 0 0 1 | * * * * 1 *
.oox3.xxo&#x ♦ 0 3 3 3 | 0 0 0 3 3 6 3 6 3 | 0 0 0 0 0 0 1 3 6 3 3 1 3 3 1 | 0 0 0 0 0 0 0 0 0 1 3 3 1 1 | * * * * * 1
```