Acronym tratet Name triangle - tetrahedron duoprism Circumradius sqrt(17/24) = 0.841625 Confer n,tet-dip

Incidence matrix according to Dynkin symbol

```x3o x3o3o

. . . . . | 12 |  2  3 | 1  6  3 | 3  6 1 | 3 2
----------+----+-------+---------+--------+----
x . . . . |  2 | 12  * | 1  3  0 | 3  3 0 | 3 1
. . x . . |  2 |  * 18 | 0  2  2 | 1  4 1 | 2 2
----------+----+-------+---------+--------+----
x3o . . . |  3 |  3  0 | 4  *  * | 3  0 0 | 3 0
x . x . . |  4 |  2  2 | * 18  * | 1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 12 | 0  2 1 | 1 2
----------+----+-------+---------+--------+----
x3o x . . ♦  6 |  6  3 | 2  3  0 | 6  * * | 2 0
x . x3o . ♦  6 |  3  6 | 0  3  2 | * 12 * | 1 1
. . x3o3o ♦  4 |  0  6 | 0  0  4 | *  * 3 | 0 2
----------+----+-------+---------+--------+----
x3o x3o . ♦  9 |  9  9 | 3  9  3 | 3  3 0 | 4 *
x . x3o3o ♦  8 |  4 12 | 0  6  8 | 0  4 2 | * 3
```

```xx3oo ox3oo&#x   → height = sqrt(2/3) = 0.816497
({3} || triddip)

o.3o. o.3o.    | 3 * | 2 3 0 0 | 1 6 3 0 0 0 | 3 6 1 0 0 | 3 2 0
.o3.o .o3.o    | * 9 | 0 1 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
---------------+-----+---------+-------------+-----------+------
x. .. .. ..    | 2 0 | 3 * * * | 1 3 0 0 0 0 | 3 3 0 0 0 | 3 1 0
oo3oo oo3oo&#x | 1 1 | * 9 * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.x .. .. ..    | 0 2 | * * 9 * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x ..    | 0 2 | * * * 9 | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
---------------+-----+---------+-------------+-----------+------
x.3o. .. ..    | 3 0 | 3 0 0 0 | 1 * * * * * | 3 0 0 0 0 | 3 0 0
xx .. .. ..&#x | 2 2 | 1 2 1 0 | * 9 * * * * | 1 2 0 0 0 | 2 1 0
.. .. ox ..&#x | 1 2 | 0 2 0 1 | * * 9 * * * | 0 2 1 0 0 | 1 2 0
.x3.o .. ..    | 0 3 | 0 0 3 0 | * * * 3 * * | 1 0 0 2 0 | 2 0 1
.x .. .x ..    | 0 4 | 0 0 2 2 | * * * * 9 * | 0 1 0 1 1 | 1 1 1
.. .. .x3.o    | 0 3 | 0 0 0 3 | * * * * * 3 | 0 0 1 0 2 | 0 2 1
---------------+-----+---------+-------------+-----------+------
xx3oo .. ..&#x ♦ 3 3 | 3 3 3 0 | 1 3 0 1 0 0 | 3 * * * * | 2 0 0
xx .. ox ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 0 1 0 | * 9 * * * | 1 1 0
.. .. ox3oo&#x ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * 3 * * | 0 2 0
.x3.o .x ..    ♦ 0 6 | 0 0 6 3 | 0 0 0 2 3 0 | * * * 3 * | 1 0 1
.x .. .x3.o    ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 2 | * * * * 3 | 0 1 1
---------------+-----+---------+-------------+-----------+------
xx3oo ox ..&#x ♦ 3 6 | 3 6 6 3 | 1 6 3 2 3 0 | 2 3 0 1 0 | 3 * *
xx .. ox3oo&#x ♦ 2 6 | 1 6 3 6 | 0 3 6 0 3 2 | 0 3 2 0 1 | * 3 *
.x3.o .x3.o    ♦ 0 9 | 0 0 9 9 | 0 0 0 3 9 3 | 0 0 0 3 3 | * * 1
```

```ox xx3oo3oo&#x   → height = sqrt(3)/2 = 0.866025
(tet || tepe)

o. o.3o.3o.    | 4 * | 3 2 0  0 | 3 1  6 0 0 | 1 3 6 0 0 | 3 2 0
.o .o3.o3.o    | * 8 | 0 1 1  3 | 0 1  3 3 3 | 0 3 3 3 1 | 3 1 1
---------------+-----+----------+------------+-----------+------
.. x. .. ..    | 2 0 | 6 * *  * | 2 0  2 0 0 | 1 1 4 0 0 | 2 2 0
oo oo3oo3oo&#x | 1 1 | * 8 *  * | 0 1  3 0 0 | 0 3 3 0 0 | 3 1 0
.x .. .. ..    | 0 2 | * * 4  * | 0 1  0 3 0 | 0 3 0 3 0 | 3 0 1
.. .x .. ..    | 0 2 | * * * 12 | 0 0  1 1 2 | 0 1 2 2 1 | 2 1 1
---------------+-----+----------+------------+-----------+------
.. x.3o. ..    | 3 0 | 3 0 0  0 | 4 *  * * * | 1 0 2 0 0 | 1 2 0
ox .. .. ..&#x | 1 2 | 0 2 1  0 | * 4  * * * | 0 3 0 0 0 | 3 0 0
.. xx .. ..&#x | 2 2 | 1 2 0  1 | * * 12 * * | 0 1 2 0 0 | 2 1 0
.x .x .. ..    | 0 4 | 0 0 2  2 | * *  * 6 * | 0 1 0 2 0 | 2 0 1
.. .x3.o ..    | 0 3 | 0 0 0  3 | * *  * * 8 | 0 0 1 1 1 | 1 1 1
---------------+-----+----------+------------+-----------+------
.. x.3o.3o.    ♦ 4 0 | 6 0 0  0 | 4 0  0 0 0 | 1 * * * * | 0 2 0
ox xx .. ..&#x ♦ 2 4 | 1 4 2  2 | 0 2  2 1 0 | * 6 * * * | 2 0 0
.. xx3oo ..&#x ♦ 3 3 | 3 3 0  3 | 1 0  3 0 1 | * * 8 * * | 1 1 0
.x .x3.o ..    ♦ 0 6 | 0 0 3  6 | 0 0  0 3 2 | * * * 4 * | 1 0 1
.. .x3.o3.o    ♦ 0 4 | 0 0 0  6 | 0 0  0 0 4 | * * * * 2 | 0 1 1
---------------+-----+----------+------------+-----------+------
ox xx3oo ..&#x ♦ 3 6 | 3 6 3  6 | 1 3  6 3 2 | 0 3 2 1 0 | 4 * *
.. xx3oo3oo&#x ♦ 4 4 | 6 4 0  6 | 4 0  6 0 4 | 1 0 4 0 1 | * 2 *
.x .x3.o3.o    ♦ 0 8 | 0 0 4 12 | 0 0  0 6 8 | 0 0 0 4 2 | * * 1
```

```xxoo xoox3oooo&#xr   → height(1,2) = height(3,4) = sqrt(2/3) = 0.816497
height(2,3) = height(4,1) = sqrt(3)/2 = 0.866025
(trip || (line || perp {3}) || pt)

o... o...3o...     | 6 * * * | 1 2 1 1 0 0 0 0 | 2 1 1 2 1 2 1 0 0 0 | 1 2 1 2 1 1 2 0 | 1 1 2 1
.o.. .o..3.o..     | * 2 * * | 0 0 3 0 1 1 0 0 | 0 0 3 3 0 0 3 1 0 0 | 0 3 1 0 0 3 3 0 | 1 0 3 1
..o. ..o.3..o.     | * * 3 * | 0 0 0 2 0 0 2 1 | 0 0 0 0 1 4 2 0 1 2 | 0 0 0 2 2 1 4 1 | 0 1 2 2
...o ...o3...o     | * * * 1 | 0 0 0 0 0 2 0 3 | 0 0 0 0 0 0 6 1 0 3 | 0 0 0 0 0 3 6 1 | 0 0 3 2
-------------------+---------+-----------------+---------------------+-----------------+--------
x... .... ....     | 2 0 0 0 | 3 * * * * * * * | 2 0 1 0 1 0 0 0 0 0 | 1 2 0 2 0 1 0 0 | 1 1 2 0
.... x... ....     | 2 0 0 0 | * 6 * * * * * * | 1 1 0 1 0 1 0 0 0 0 | 1 1 1 1 1 0 1 0 | 1 1 1 1
oo.. oo..3oo..&#x  | 1 1 0 0 | * * 6 * * * * * | 0 0 1 2 0 0 1 0 0 0 | 0 2 1 0 0 1 2 0 | 1 0 2 1
o.o. o.o.3o.o.&#x  | 1 0 1 0 | * * * 6 * * * * | 0 0 0 0 1 2 1 0 0 0 | 0 0 0 2 1 1 2 0 | 0 1 2 1
.x.. .... ....     | 0 2 0 0 | * * * * 1 * * * | 0 0 3 0 0 0 0 1 0 0 | 0 3 0 0 0 3 0 0 | 1 0 3 0
.o.o .o.o3.o.o&#x  | 0 1 0 1 | * * * * * 2 * * | 0 0 0 0 0 0 3 1 0 0 | 0 0 0 0 0 3 3 0 | 0 0 3 1
.... ..x. ....     | 0 0 2 0 | * * * * * * 3 * | 0 0 0 0 0 2 0 0 1 1 | 0 0 0 1 2 0 2 1 | 0 1 1 2
..oo ..oo3..oo&#x  | 0 0 1 1 | * * * * * * * 3 | 0 0 0 0 0 0 2 0 0 2 | 0 0 0 0 0 1 4 1 | 0 0 2 2
-------------------+---------+-----------------+---------------------+-----------------+--------
x... x... ....     | 4 0 0 0 | 2 2 0 0 0 0 0 0 | 3 * * * * * * * * * | 1 1 0 1 0 0 0 0 | 1 1 1 0
.... x...3o...     | 3 0 0 0 | 0 3 0 0 0 0 0 0 | * 2 * * * * * * * * | 1 0 1 0 1 0 0 0 | 1 1 0 1
xx.. .... ....&#x  | 2 2 0 0 | 1 0 2 0 1 0 0 0 | * * 3 * * * * * * * | 0 2 0 0 0 1 0 0 | 1 0 2 0
.... xo.. ....&#x  | 2 1 0 0 | 0 1 2 0 0 0 0 0 | * * * 6 * * * * * * | 0 1 1 0 0 0 1 0 | 1 0 1 1
x.o. .... ....&#x  | 2 0 1 0 | 1 0 0 2 0 0 0 0 | * * * * 3 * * * * * | 0 0 0 2 0 1 0 0 | 0 1 2 0
.... x.x. ....&#x  | 2 0 2 0 | 0 1 0 2 0 0 1 0 | * * * * * 6 * * * * | 0 0 0 1 1 0 1 0 | 0 1 1 1
oooo oooo3oooo&#xr | 1 1 1 1 | 0 0 1 1 0 1 0 1 | * * * * * * 6 * * * | 0 0 0 0 0 1 2 0 | 0 0 2 1
.x.o .... ....&#x  | 0 2 0 1 | 0 0 0 0 1 2 0 0 | * * * * * * * 1 * * | 0 0 0 0 0 3 0 0 | 0 0 3 0
.... ..x.3..o.     | 0 0 3 0 | 0 0 0 0 0 0 3 0 | * * * * * * * * 1 * | 0 0 0 0 2 0 0 1 | 0 1 0 2
.... ..xo ....&#x  | 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * * * * * 3 | 0 0 0 0 0 0 2 1 | 0 0 1 2
-------------------+---------+-----------------+---------------------+-----------------+--------
x... x...3o...     ♦ 6 0 0 0 | 3 6 0 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 | 1 * * * * * * * | 1 1 0 0
xx.. xo.. ....&#x  ♦ 4 2 0 0 | 2 2 4 0 1 0 0 0 | 1 0 2 2 0 0 0 0 0 0 | * 3 * * * * * * | 1 0 1 0
.... xo..3oo..&#x  ♦ 3 1 0 0 | 0 3 3 0 0 0 0 0 | 0 1 0 3 0 0 0 0 0 0 | * * 2 * * * * * | 1 0 0 1
x.o. x.x. ....&#x  ♦ 4 0 2 0 | 2 2 0 4 0 0 1 0 | 1 0 0 0 2 2 0 0 0 0 | * * * 3 * * * * | 0 1 1 0
.... x.x.3o.o.&#x  ♦ 3 0 3 0 | 0 3 0 3 0 0 3 0 | 0 1 0 0 0 3 0 0 1 0 | * * * * 2 * * * | 0 1 0 1
xxoo .... ....&#xr ♦ 2 2 1 1 | 1 0 2 2 1 2 0 1 | 0 0 1 0 1 0 2 1 0 0 | * * * * * 3 * * | 0 0 2 0
.... xoox ....&#xr ♦ 2 1 2 1 | 0 1 2 2 0 1 1 2 | 0 0 0 1 0 1 2 0 0 1 | * * * * * * 6 * | 0 0 1 1
.... ..xo3..oo&#x  ♦ 0 0 3 1 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 1 3 | * * * * * * * 1 | 0 0 0 2
-------------------+---------+-----------------+---------------------+-----------------+--------
xx.. xo..3oo..&#x  ♦ 6 2 0 0 | 3 6 6 0 1 0 0 0 | 3 2 3 6 0 0 0 0 0 0 | 1 3 2 0 0 0 0 0 | 1 * * *
x.o. x.x.3o.o.&#x  ♦ 6 0 3 0 | 3 6 0 6 0 0 3 0 | 3 2 0 0 3 6 0 0 1 0 | 1 0 0 3 2 0 0 0 | * 1 * *
xxoo xoox ....&#xr ♦ 4 2 2 1 | 2 2 4 4 1 2 1 2 | 1 0 2 2 2 2 4 1 0 1 | 0 1 0 1 0 2 2 0 | * * 3 *
.... xoox3oooo&#xr ♦ 3 1 3 1 | 0 3 3 3 0 1 3 3 | 0 1 0 3 0 3 3 0 1 3 | 0 0 1 0 1 0 3 1 | * * * 2
```

```ox xo xx3oo&#x   → height = 1/sqrt(2) = 0.707107
(trip || lacing-ortho trip)

o. o. o.3o.    | 6 * | 1 2  2 0 0 | 2 1 1 2  4 0 0 | 1 1 2 4 2 0 | 2 1 2
.o .o .o3.o    | * 6 | 0 0  2 1 2 | 0 0 2 1  4 2 1 | 0 1 4 2 2 1 | 2 2 1
---------------+-----+------------+----------------+-------------+------
.. x. .. ..    | 2 0 | 3 *  * * * | 2 0 0 2  0 0 0 | 1 1 0 2 0 0 | 2 0 2
.. .. x. ..    | 2 0 | * 6  * * * | 1 1 0 0  2 0 0 | 1 0 1 2 2 0 | 1 1 2
oo oo oo3oo&#x | 1 1 | * * 12 * * | 0 0 1 1  2 0 0 | 0 1 2 2 1 0 | 2 1 1
.x .. .. ..    | 0 2 | * *  * 3 * | 0 0 2 0  0 2 0 | 0 1 4 0 0 1 | 2 2 0
.. .. .x ..    | 0 2 | * *  * * 6 | 0 0 0 0  2 1 1 | 0 0 2 1 2 1 | 1 2 1
---------------+-----+------------+----------------+-------------+------
.. x. x. ..    | 4 0 | 2 2  0 0 0 | 3 * * *  * * * | 1 0 0 2 0 0 | 1 0 2
.. .. x.3o.    | 3 0 | 0 3  0 0 0 | * 2 * *  * * * | 1 0 0 0 2 0 | 0 1 2
ox .. .. ..&#x | 1 2 | 0 0  2 1 0 | * * 6 *  * * * | 0 1 2 0 0 0 | 2 1 0
.. xo .. ..&#x | 2 1 | 1 0  2 0 0 | * * * 6  * * * | 0 1 0 2 0 0 | 2 0 1
.. .. xx ..&#x | 2 2 | 0 1  2 0 1 | * * * * 12 * * | 0 0 1 1 1 0 | 1 1 1
.x .. .x ..    | 0 4 | 0 0  0 2 2 | * * * *  * 3 * | 0 0 2 0 0 1 | 1 2 0
.. .. .x3.o    | 0 3 | 0 0  0 0 3 | * * * *  * * 2 | 0 0 0 0 2 1 | 0 2 1
---------------+-----+------------+----------------+-------------+------
.. x. x.3o.    ♦ 6 0 | 3 6  0 0 0 | 3 2 0 0  0 0 0 | 1 * * * * * | 0 0 2
ox xo .. ..&#x ♦ 2 2 | 1 0  4 1 0 | 0 0 2 2  0 0 0 | * 3 * * * * | 2 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1  4 2 2 | 0 0 2 0  2 1 0 | * * 6 * * * | 1 1 0
.. xo xx ..&#x ♦ 4 2 | 2 2  4 0 1 | 1 0 0 2  2 0 0 | * * * 6 * * | 1 0 1
.. .. xx3oo&#x ♦ 3 3 | 0 3  3 0 3 | 0 1 0 0  3 0 1 | * * * * 4 * | 0 1 1
.x .. .x3.o    ♦ 0 6 | 0 0  0 3 6 | 0 0 0 0  0 3 2 | * * * * * 1 | 0 2 0
---------------+-----+------------+----------------+-------------+------
ox xo xx ..&#x ♦ 4 4 | 2 2  8 2 2 | 1 0 4 4  4 1 0 | 0 2 2 2 0 0 | 3 * *
ox .. xx3oo&#x ♦ 3 6 | 0 3  6 3 6 | 0 1 3 0  6 3 2 | 0 0 3 0 2 1 | * 2 *
.. xo xx3oo&#x ♦ 6 3 | 3 6  6 0 3 | 3 2 0 3  6 0 1 | 1 0 0 3 2 0 | * * 2
```

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