Acronym squatet Name square-tetrahedron duoprism Circumradius sqrt(7/8) = 0.935414 Confer n,tet-dip

Incidence matrix according to Dynkin symbol

```x4o x3o3o

. . . . . | 16 |  2  3 | 1  6  3 | 3  6 1 | 3 2
----------+----+-------+---------+--------+----
x . . . . |  2 | 16  * | 1  3  0 | 3  3 0 | 3 1
. . x . . |  2 |  * 24 | 0  2  2 | 1  4 1 | 2 2
----------+----+-------+---------+--------+----
x4o . . . |  4 |  4  0 | 4  *  * | 3  0 0 | 3 0
x . x . . |  4 |  2  2 | * 24  * | 1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 16 | 0  2 1 | 1 2
----------+----+-------+---------+--------+----
x4o x . . ♦  8 |  8  4 | 2  4  0 | 6  * * | 2 0
x . x3o . ♦  6 |  3  6 | 0  3  2 | * 16 * | 1 1
. . x3o3o ♦  4 |  0  6 | 0  0  4 | *  * 4 | 0 2
----------+----+-------+---------+--------+----
x4o x3o . ♦ 12 | 12 12 | 3 12  4 | 3  4 0 | 4 *
x . x3o3o ♦  8 |  4 12 | 0  6  8 | 0  4 2 | * 4
```

```x x x3o3o

. . . . . | 16 | 1 1  3 | 1  3  3  3 | 3 3 3 1 | 3 1 1
----------+----+--------+------------+---------+------
x . . . . |  2 | 8 *  * | 1  3  0  0 | 3 3 0 0 | 3 1 0
. x . . . |  2 | * 8  * | 1  0  3  0 | 3 0 3 0 | 3 0 1
. . x . . |  2 | * * 24 | 0  1  1  2 | 1 2 2 1 | 2 1 1
----------+----+--------+------------+---------+------
x x . . . |  4 | 2 2  0 | 4  *  *  * | 3 0 0 0 | 3 0 0
x . x . . |  4 | 1 0  2 | * 12  *  * | 1 2 0 0 | 2 1 0
. x x . . |  4 | 0 1  2 | *  * 12  * | 1 0 2 0 | 2 0 1
. . x3o . |  3 | 0 0  3 | *  *  * 16 | 0 1 1 1 | 1 1 1
----------+----+--------+------------+---------+------
x x x . . ♦  8 | 4 4  4 | 2  2  2  0 | 6 * * * | 2 0 0
x . x3o . ♦  6 | 3 0  6 | 0  3  0  2 | * 8 * * | 1 1 0
. x x3o . ♦  6 | 3 0  6 | 0  3  0  2 | * * 8 * | 1 0 1
. . x3o3o ♦  4 | 0 0  6 | 0  0  0  4 | * * * 4 | 0 1 1
----------+----+--------+------------+---------+------
x x x3o . ♦ 12 | 6 6 12 | 3  6  6  4 | 3 2 2 0 | 4 * *
x . x3o3o ♦  8 | 4 0 12 | 0  6  0  8 | 0 4 0 2 | * 2 *
. x x3o3o ♦  8 | 4 0 12 | 0  6  0  8 | 0 4 0 2 | * * 2
```

```ox3oo xx4oo&#x   → height = sqrt(2/3) = 0.816497
({4} || tisdip)

o.3o. o.4o.    | 4  * | 2  3  0  0 | 1  3  6 0  0 0 | 1  6 3 0 0 | 2 3 0
.o3.o .o4.o    | * 12 | 0  1  2  2 | 0  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
---------------+------+------------+----------------+------------+------
.. .. x. ..    | 2  0 | 4  *  *  * | 1  0  3 0  0 0 | 0  3 3 0 0 | 1 3 0
oo3oo oo4oo&#x | 1  1 | * 12  *  * | 0  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x .. .. ..    | 0  2 | *  * 12  * | 0  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
.. .. .x ..    | 0  2 | *  *  * 12 | 0  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
---------------+------+------------+----------------+------------+------
.. .. x.4o.    | 4  0 | 4  0  0  0 | 1  *  * *  * * | 0  0 3 0 0 | 0 3 0
ox .. .. ..&#x | 1  2 | 0  2  1  0 | * 12  * *  * * | 1  2 0 0 0 | 2 1 0
.. .. xx ..&#x | 2  2 | 1  2  0  1 | *  * 12 *  * * | 0  2 1 0 0 | 1 2 0
.x3.o .. ..    | 0  3 | 0  0  3  0 | *  *  * 4  * * | 1  0 0 2 0 | 2 0 1
.x .. .x ..    | 0  4 | 0  0  2  2 | *  *  * * 12 * | 0  1 0 1 1 | 1 1 1
.. .. .x4.o    | 0  4 | 0  0  0  4 | *  *  * *  * 3 | 0  0 1 0 2 | 0 2 1
---------------+------+------------+----------------+------------+------
ox3oo .. ..&#x ♦ 1  3 | 0  3  3  0 | 0  3  0 1  0 0 | 4  * * * * | 2 0 0
ox .. xx ..&#x ♦ 2  4 | 1  4  2  2 | 0  2  2 0  1 0 | * 12 * * * | 1 1 0
.. .. xx4oo&#x ♦ 4  4 | 4  4  0  4 | 1  0  4 0  0 1 | *  * 3 * * | 0 2 0
.x3.o .x ..    ♦ 0  6 | 0  0  6  3 | 0  0  0 2  3 0 | *  * * 4 * | 1 0 1
.x .. .x4.o    ♦ 0  8 | 0  0  4  8 | 0  0  0 0  4 2 | *  * * * 3 | 0 1 1
---------------+------+------------+----------------+------------+------
ox3oo xx ..    ♦ 2  6 | 1  6  6  3 | 0  6  3 2  3 0 | 2  3 0 1 0 | 4 * *
ox .. xx4oo&#x ♦ 4  8 | 4  8  4  8 | 1  4  8 0  4 2 | 0  4 2 0 1 | * 3 *
.x3.o .x4.o    ♦ 0 12 | 0  0 12 12 | 0  0  0 4 12 3 | 0  0 0 4 3 | * * 1
```

```ox xo xx4oo&#x   → height = 1/sqrt(2) = 0.707107
(cube || lacing-ortho cube)

o. o. o.4o.    | 8 * | 1 2  2 0 0 | 2 1 1 2  4 0 0 | 1 1 2 4 2 0 | 2 1 2
.o .o .o4.o    | * 8 | 0 0  2 1 2 | 0 0 2 1  4 2 1 | 0 1 4 2 2 1 | 2 2 1
---------------+-----+------------+----------------+-------------+------
.. x. .. ..    | 2 0 | 4 *  * * * | 2 0 0 2  0 0 0 | 1 1 0 2 0 0 | 2 0 2
.. .. x. ..    | 2 0 | * 8  * * * | 1 1 0 0  2 0 0 | 1 0 1 2 2 0 | 1 1 2
oo oo oo4oo&#x | 1 1 | * * 16 * * | 0 0 1 1  2 0 0 | 0 1 2 2 1 0 | 2 1 1
.x .. .. ..    | 0 2 | * *  * 4 * | 0 0 2 0  0 2 0 | 0 1 4 0 0 1 | 2 2 0
.. .. .x ..    | 0 2 | * *  * * 8 | 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 | 4 * * *  * * * | 1 0 0 2 0 0 | 1 0 2
.. .. x.4o.    | 4 0 | 0 4  0 0 0 | * 2 * *  * * * | 1 0 0 0 2 0 | 0 1 2
ox .. .. ..&#x | 1 2 | 0 0  2 1 0 | * * 8 *  * * * | 0 1 2 0 0 0 | 2 1 0
.. xo .. ..&#x | 2 1 | 1 0  2 0 0 | * * * 8  * * * | 0 1 0 2 0 0 | 2 0 1
.. .. xx ..&#x | 2 2 | 0 1  2 0 1 | * * * * 16 * * | 0 0 1 1 1 0 | 1 1 1
.x .. .x ..    | 0 4 | 0 0  0 2 2 | * * * *  * 4 * | 0 0 2 0 0 1 | 1 2 0
.. .. .x4.o    | 0 4 | 0 0  0 0 4 | * * * *  * * 2 | 0 0 0 0 2 1 | 0 2 1
---------------+-----+------------+----------------+-------------+------
.. x. x.4o.    ♦ 8 0 | 4 8  0 0 0 | 4 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 | * 4 * * * * | 2 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1  4 2 2 | 0 0 2 0  2 1 0 | * * 8 * * * | 1 1 0
.. xo xx ..&#x ♦ 4 2 | 2 2  4 0 1 | 1 0 0 2  2 0 0 | * * * 8 * * | 1 0 1
.. .. xx4oo&#x ♦ 4 4 | 0 4  4 0 4 | 0 1 0 0  4 0 1 | * * * * 4 * | 0 1 1
.x .. .x4.o    ♦ 0 8 | 0 0  0 4 8 | 0 0 0 0  0 4 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 | 4 * *
ox .. xx4oo&#x ♦ 4 8 | 0 4  8 4 8 | 0 1 4 0  8 4 2 | 0 0 4 0 2 1 | * 2 *
.. xo xx4oo&#x ♦ 8 4 | 4 8  8 0 4 | 4 2 0 4  8 0 1 | 1 0 0 4 2 0 | * * 2
```