Acronym troct Name triangle-octahedron duoprism Circumradius sqrt(5/6) = 0.912871 Confer n,oct-dip

Incidence matrix according to Dynkin symbol

```x3o x3o4o

. . . . . | 18 |  2  4 | 1  8  4 |  4  8 1 | 4 2
----------+----+-------+---------+---------+----
x . . . . |  2 | 18  * | 1  4  0 |  4  4 0 | 4 1
. . x . . |  2 |  * 36 | 0  2  2 |  1  4 1 | 2 2
----------+----+-------+---------+---------+----
x3o . . . |  3 |  3  0 | 6  *  * |  4  0 0 | 4 0
x . x . . |  4 |  2  2 | * 36  * |  1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 24 |  0  2 1 | 1 2
----------+----+-------+---------+---------+----
x3o x . . ♦  6 |  6  3 | 2  3  0 | 12  * * | 2 0
x . x3o . ♦  6 |  3  6 | 0  3  2 |  * 24 * | 1 1
. . x3o4o ♦  6 |  0 12 | 0  0  8 |  *  * 3 | 0 2
----------+----+-------+---------+---------+----
x3o x3o . ♦  9 |  9  9 | 3  9  3 |  3  3 0 | 8 *
x . x3o4o ♦ 12 |  6 24 | 0 12 16 |  0  8 2 | * 3
```

```x3o o3x3o

. . . . . | 18 |  2  4 | 1  8  2  2 |  4  4  4 1 | 2 2 2
----------+----+-------+------------+------------+------
x . . . . |  2 | 18  * | 1  4  0  0 |  4  2  2 0 | 2 2 1
. . . x . |  2 |  * 36 | 0  2  1  1 |  1  2  2 1 | 1 1 2
----------+----+-------+------------+------------+------
x3o . . . |  3 |  3  0 | 6  *  *  * |  4  0  0 0 | 2 2 0
x . . x . |  4 |  2  2 | * 36  *  * |  1  1  1 0 | 1 1 1
. . o3x . |  3 |  0  3 | *  * 12  * |  0  2  0 1 | 1 0 2
. . . x3o |  3 |  0  3 | *  *  * 12 |  0  0  2 1 | 0 1 2
----------+----+-------+------------+------------+------
x3o . x . ♦  6 |  6  3 | 2  3  0  0 | 12  *  * * | 1 1 0
x . o3x . ♦  6 |  3  6 | 0  3  2  0 |  * 12  * * | 1 0 1
x . . x3o ♦  6 |  3  6 | 0  3  0  2 |  *  * 12 * | 0 1 1
. . o3x3o ♦  6 |  0 12 | 0  0  4  4 |  *  *  * 3 | 0 0 2
----------+----+-------+------------+------------+------
x3o o3x . ♦  9 |  9  9 | 3  9  3  0 |  3  3  0 0 | 4 * *
x3o . x3o ♦  9 |  9  9 | 3  9  0  3 |  3  0  3 0 | * 4 *
x . o3x3o ♦ 12 |  6 24 | 0 12  8  8 |  0  4  4 2 | * * 3
```

```xo3ox xx3oo&#x   → height = sqrt(2/3) = 0.816497
(triddip || gyro triddip)

o.3o. o.3o.    | 9 * | 2 2  2 0 0 | 1 4 1 2 1  4 0 0 0 | 2 2 1 4 2 2 0 0 | 1 2 2 1 0
.o3.o .o3.o    | * 9 | 0 0  2 2 2 | 0 0 0 1 2  4 1 4 1 | 0 0 1 2 4 2 2 2 | 0 2 1 2 1
---------------+-----+------------+--------------------+-----------------+----------
x. .. .. ..    | 2 0 | 9 *  * * * | 1 2 0 1 0  0 0 0 0 | 2 1 1 2 0 0 0 0 | 1 2 1 0 0
.. .. x. ..    | 2 0 | * 9  * * * | 0 2 1 0 0  2 0 0 0 | 1 2 0 2 1 2 0 0 | 1 2 2 1 0
oo3oo oo3oo&#x | 1 1 | * * 18 * * | 0 0 0 1 1  2 0 0 0 | 0 0 1 2 2 1 0 0 | 0 1 1 1 0
.. .x .. ..    | 0 2 | * *  * 9 * | 0 0 0 0 1  0 1 2 0 | 0 0 1 0 2 0 2 1 | 0 2 0 1 1
.. .. .x ..    | 0 2 | * *  * * 9 | 0 0 0 0 0  2 0 2 1 | 0 0 0 1 2 2 1 2 | 0 2 1 2 1
---------------+-----+------------+--------------------+-----------------+----------
x.3o. .. ..    | 3 0 | 3 0  0 0 0 | 3 * * * *  * * * * | 2 0 1 0 0 0 0 0 | 1 2 0 0 0
x. .. x. ..    | 4 0 | 2 2  0 0 0 | * 9 * * *  * * * * | 1 1 0 1 0 0 0 0 | 1 1 1 0 0
.. .. x.3o.    | 3 0 | 0 3  0 0 0 | * * 3 * *  * * * * | 0 2 0 0 0 2 0 0 | 1 0 2 1 0
xo .. .. ..&#x | 2 1 | 1 0  2 0 0 | * * * 9 *  * * * * | 0 0 1 2 0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x | 1 2 | 0 0  2 1 0 | * * * * 9  * * * * | 0 0 1 0 2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x | 2 2 | 0 1  2 0 1 | * * * * * 18 * * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 0
.o3.x .. ..    | 0 3 | 0 0  0 3 0 | * * * * *  * 3 * * | 0 0 1 0 0 0 2 0 | 0 2 0 0 1
.. .x .x ..    | 0 4 | 0 0  0 2 2 | * * * * *  * * 9 * | 0 0 0 0 1 0 1 1 | 0 1 0 1 1
.. .. .x3.o    | 0 3 | 0 0  0 0 3 | * * * * *  * * * 3 | 0 0 0 0 0 2 0 2 | 0 0 1 2 1
---------------+-----+------------+--------------------+-----------------+----------
x.3o. x. ..    ♦ 6 0 | 6 3  0 0 0 | 2 3 0 0 0  0 0 0 0 | 3 * * * * * * * | 1 1 0 0 0
x. .. x.3o.    ♦ 6 0 | 3 6  0 0 0 | 0 3 2 0 0  0 0 0 0 | * 3 * * * * * * | 1 0 1 0 0
xo3ox .. ..&#x ♦ 3 3 | 3 0  6 3 0 | 1 0 0 3 3  0 1 0 0 | * * 3 * * * * * | 0 2 0 0 0
xo .. xx ..&#x ♦ 4 2 | 2 2  4 0 1 | 0 1 0 2 0  2 0 0 0 | * * * 9 * * * * | 0 1 1 0 0
.. ox xx ..&#x ♦ 2 4 | 0 1  4 2 2 | 0 0 0 0 2  2 0 1 0 | * * * * 9 * * * | 0 1 0 1 0
.. .. xx3oo&#x ♦ 3 3 | 0 3  3 0 3 | 0 0 1 0 0  3 0 0 1 | * * * * * 6 * * | 0 0 1 1 0
.o3.x .x ..    ♦ 0 6 | 0 0  0 6 3 | 0 0 0 0 0  0 2 3 0 | * * * * * * 3 * | 0 1 0 0 1
.. .x .x3.o    ♦ 0 6 | 0 0  0 3 6 | 0 0 0 0 0  0 0 3 2 | * * * * * * * 3 | 0 0 0 1 1
---------------+-----+------------+--------------------+-----------------+----------
x.3o. x.3o.    ♦ 9 0 | 9 9  0 0 0 | 3 9 3 0 0  0 0 0 0 | 3 3 0 0 0 0 0 0 | 1 * * * *
xo3ox xx ..&#x ♦ 6 6 | 6 6  6 6 6 | 2 3 0 6 6  6 2 3 0 | 1 0 2 3 3 0 1 0 | * 3 * * *
xo .. xx3oo&#x ♦ 6 3 | 3 6  6 0 3 | 0 3 2 3 0  6 0 0 1 | 0 1 0 3 0 2 0 0 | * * 3 * *
.. ox xx3oo&#x ♦ 3 6 | 0 3  6 3 6 | 0 0 1 0 3  6 0 3 2 | 0 0 0 0 3 2 0 1 | * * * 3 *
.o3.x .x3.o    ♦ 0 9 | 0 0  0 9 9 | 0 0 0 0 0  0 3 9 3 | 0 0 0 0 0 0 3 3 | * * * * 1
```

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