Acronym squoct Name square-octahedron duoprism,vertex figure of brinoh Circumradius 1 Volume sqrt(2)/3 = 0.471405 Confer more general: n,oct-dip   (n,m-ap)-dip   segmentotera: squasquippy   general polytopal classes: segmentotera   lace simplices   Hanner polytopes Externallinks

Incidence matrix according to Dynkin symbol

```x4o x3o4o

. . . . . | 24 |  2  4 | 1  8  4 |  4  8 1 | 4 2
----------+----+-------+---------+---------+----
x . . . . |  2 | 24  * | 1  4  0 |  4  4 0 | 4 1
. . x . . |  2 |  * 48 | 0  2  2 |  1  4 1 | 2 2
----------+----+-------+---------+---------+----
x4o . . . |  4 |  4  0 | 6  *  * |  4  0 0 | 4 0
x . x . . |  4 |  2  2 | * 48  * |  1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 32 |  0  2 1 | 1 2
----------+----+-------+---------+---------+----
x4o x . . ♦  8 |  8  4 | 2  4  0 | 12  * * | 2 0
x . x3o . ♦  6 |  3  6 | 0  3  2 |  * 32 * | 1 1
. . x3o4o ♦  6 |  0 12 | 0  0  8 |  *  * 4 | 0 2
----------+----+-------+---------+---------+----
x4o x3o . ♦ 12 | 12 12 | 3 12  4 |  3  4 0 | 8 *
x . x3o4o ♦ 12 |  6 24 | 0 12 16 |  0  8 2 | * 4
```

```x4o o3x3o

. . . . . | 24 |  2  4 | 1  8  2  2 |  4  4  4 1 | 2 2 2
----------+----+-------+------------+------------+------
x . . . . |  2 | 24  * | 1  4  0  0 |  4  2  2 0 | 2 2 1
. . . x . |  2 |  * 48 | 0  2  1  1 |  1  2  2 1 | 1 1 2
----------+----+-------+------------+------------+------
x4o . . . |  4 |  4  0 | 6  *  *  * |  4  0  0 0 | 2 2 0
x . . x . |  4 |  2  2 | * 48  *  * |  1  1  1 0 | 1 1 1
. . o3x . |  3 |  0  3 | *  * 16  * |  0  2  0 1 | 1 0 2
. . . x3o |  3 |  0  3 | *  *  * 16 |  0  0  2 1 | 0 1 2
----------+----+-------+------------+------------+------
x4o . x . ♦  8 |  8  4 | 2  4  0  0 | 12  *  * * | 1 1 0
x . o3x . ♦  6 |  3  6 | 0  3  2  0 |  * 16  * * | 1 0 1
x . . x3o ♦  6 |  3  6 | 0  3  0  2 |  *  * 16 * | 0 1 1
. . o3x3o ♦  6 |  0 12 | 0  0  4  4 |  *  *  * 4 | 0 0 2
----------+----+-------+------------+------------+------
x4o o3x . ♦ 12 | 12 12 | 3 12  4  0 |  3  4  0 0 | 4 * *
x4o . x3o ♦ 12 | 12 12 | 3 12  0  4 |  3  0  4 0 | * 4 *
x . o3x3o ♦ 12 |  6 24 | 0 12  8  8 |  0  4  4 2 | * * 4
```

```x x x3o4o

. . . . . | 24 |  1  1  4 | 1  4  4  4 |  4  4  4 1 | 4 1 1
----------+----+----------+------------+------------+------
x . . . . |  2 | 12  *  * | 1  4  0  0 |  4  4  0 0 | 4 1 0
. x . . . |  2 |  * 12  * | 1  0  4  0 |  4  0  4 0 | 4 0 1
. . x . . |  2 |  *  * 48 | 0  1  1  2 |  1  2  2 1 | 2 1 1
----------+----+----------+------------+------------+------
x x . . . |  4 |  2  2  0 | 6  *  *  * |  4  0  0 0 | 4 0 0
x . x . . |  4 |  2  0  2 | * 24  *  * |  1  2  0 0 | 2 1 0
. x x . . |  4 |  0  2  2 | *  * 24  * |  1  0  2 0 | 2 0 1
. . x3o . |  3 |  0  0  3 | *  *  * 32 |  0  1  1 1 | 1 1 1
----------+----+----------+------------+------------+------
x x x . . ♦  8 |  4  4  4 | 2  2  2  0 | 12  *  * * | 2 0 0
x . x3o . ♦  6 |  3  0  6 | 0  3  0  2 |  * 16  * * | 1 1 0
. x x3o . ♦  6 |  0  3  6 | 0  0  3  2 |  *  * 16 * | 1 0 1
. . x3o4o ♦  6 |  0  0 12 | 0  0  0  8 |  *  *  * 4 | 0 1 1
----------+----+----------+------------+------------+------
x x x3o . ♦ 12 |  6  6 12 | 3  6  6  4 |  3  2  2 0 | 8 * *
x . x3o4o ♦ 12 |  6  0 24 | 0 12  0 16 |  0  8  0 2 | * 2 *
. x x3o4o ♦ 12 |  0  6 24 | 0  0 12 16 |  0  0  8 2 | * * 2
```

```x x o3x3o

. . . . . | 24 |  1  1  4 | 1  4  4  2  2 |  4 2 2 2 2 1 | 2 2 1 1
----------+----+----------+---------------+--------------+--------
x . . . . |  2 | 12  *  * | 1  4  0  0  0 |  4 2 2 0 0 0 | 2 2 1 0
. x . . . |  2 |  * 12  * | 1  0  4  0  0 |  4 0 0 2 2 0 | 2 2 0 1
. . . x . |  2 |  *  * 48 | 0  1  1  1  1 |  1 1 1 1 1 1 | 1 1 1 1
----------+----+----------+---------------+--------------+--------
x x . . . |  4 |  2  2  0 | 6  *  *  *  * |  4 0 0 0 0 0 | 2 2 0 0
x . . x . |  4 |  2  0  2 | * 24  *  *  * |  1 1 1 0 0 0 | 1 1 1 0
. x . x . |  4 |  0  2  2 | *  * 24  *  * |  1 0 0 1 1 0 | 1 1 0 1
. . o3x . |  3 |  0  0  3 | *  *  * 16  * |  0 1 0 1 1 0 | 1 0 1 1
. . . x3o |  3 |  0  0  3 | *  *  *  * 16 |  0 0 1 0 1 1 | 0 1 1 1
----------+----+----------+---------------+--------------+--------
x x . x . ♦  8 |  4  4  4 | 2  2  2  0  0 | 12 * * * * * | 1 1 0 0
x . o3x . ♦  6 |  3  0  6 | 0  3  0  2  0 |  * 8 * * * * | 1 0 1 0
x . . x3o ♦  6 |  3  0  6 | 0  3  0  0  2 |  * * 8 * * * | 0 1 0 1
. x o3x . ♦  6 |  0  3  6 | 0  0  3  2  0 |  * * * 8 * * | 1 0 1 0
. x . x3o ♦  6 |  0  3  6 | 0  0  3  0  2 |  * * * * 8 * | 0 1 0 1
. . o3x3o ♦  6 |  0  0 12 | 0  0  0  4  4 |  * * * * * 4 | 0 0 1 1
----------+----+----------+---------------+--------------+--------
x x o3x . ♦ 12 |  6  6 12 | 3  6  6  4  0 |  3 2 0 2 0 0 | 4 * * *
x x . x3o ♦ 12 |  6  6 12 | 3  6  6  0  4 |  3 0 2 0 2 0 | * 4 * *
x . o3x3o ♦ 12 |  6  0 24 | 0 12  0  8  8 |  0 4 0 4 0 2 | * * 2 *
. x o3x3o ♦ 12 |  0  6 24 | 0  0 12  8  8 |  0 0 4 0 4 2 | * * * 2
```

```xx xx3oo4oo&#x   → height = 1
(ope || ope)

o. o.3o.4o.    | 12  * | 1  4  1 0  0 |  4  4 1  4  0  0 | 4 1  4  4 0 0 | 1 4 1 0
.o .o3.o4.o    |  * 12 | 0  0  1 1  4 |  0  0 1  4  4  4 | 0 0  4  4 4 1 | 0 4 1 1
---------------+-------+--------------+------------------+---------------+--------
x. .. .. ..    |  2  0 | 6  *  * *  * |  4  0 1  0  0  0 | 4 0  4  0 0 0 | 1 4 0 0
.. x. .. ..    |  2  0 | * 24  * *  * |  1  2 0  1  0  0 | 2 1  1  2 0 0 | 1 2 1 0
oo oo3oo4oo&#x |  1  1 | *  * 12 *  * |  0  0 1  4  0  0 | 0 0  4  4 0 0 | 0 4 1 0
.x .. .. ..    |  0  2 | *  *  * 6  * |  0  0 1  0  4  0 | 0 0  4  0 4 0 | 0 4 0 1
.. .x .. ..    |  0  2 | *  *  * * 24 |  0  0 0  1  1  2 | 0 0  1  2 2 1 | 0 2 1 1
---------------+-------+--------------+------------------+---------------+--------
x. x. .. ..    |  4  0 | 2  2  0 0  0 | 12  * *  *  *  * | 2 0  1  0 0 0 | 1 2 0 0
.. x.3o. ..    |  3  0 | 0  3  0 0  0 |  * 16 *  *  *  * | 1 1  0  1 0 0 | 1 1 1 0
xx .. .. ..&#x |  2  2 | 1  0  2 1  0 |  *  * 6  *  *  * | 0 0  4  0 0 0 | 0 4 0 0
.. xx .. ..&#x |  2  2 | 0  1  2 0  1 |  *  * * 24  *  * | 0 0  1  2 0 0 | 0 2 1 0
.x .x .. ..    |  0  4 | 0  0  0 2  2 |  *  * *  * 12  * | 0 0  1  0 2 0 | 0 2 0 1
.. .x3.o ..    |  0  3 | 0  0  0 0  3 |  *  * *  *  * 16 | 0 0  0  1 1 1 | 0 1 1 1
---------------+-------+--------------+------------------+---------------+--------
x. x.3o. ..    ♦  6  0 | 3  6  0 0  0 |  3  2 0  0  0  0 | 8 *  *  * * * | 1 1 0 0
.. x.3o.4o.    ♦  6  0 | 0 12  0 0  0 |  0  8 0  0  0  0 | * 2  *  * * * | 1 0 1 0
xx xx .. ..&#x ♦  4  4 | 2  2  4 2  2 |  1  0 2  2  1  0 | * * 12  * * * | 0 2 0 0
.. xx3oo ..&#x ♦  3  3 | 0  3  3 0  3 |  0  1 0  3  0  1 | * *  * 16 * * | 0 1 1 0
.x .x3.o ..    ♦  0  6 | 0  0  0 3  6 |  0  0 0  0  3  2 | * *  *  * 8 * | 0 1 0 1
.. .x3.o4.o    ♦  0  6 | 0  0  0 0 12 |  0  0 0  0  0  8 | * *  *  * * 2 | 0 0 1 1
---------------+-------+--------------+------------------+---------------+--------
x. x.3o.4o.    ♦ 12  0 | 6 24  0 0  0 | 12 16 0  0  0  0 | 8 2  0  0 0 0 | 1 * * *
xx xx3oo ..&#x ♦  6  6 | 3  6  6 3  6 |  3  2 3  6  3  2 | 1 0  3  2 1 0 | * 8 * *
.. xx3oo4oo&#x ♦  6  6 | 0 12  6 0 12 |  0  8 0 12  0  8 | 0 1  0  8 0 1 | * * 2 *
.x .x3.o4.o    ♦  0 12 | 0  0  0 6 24 |  0  0 0  0 12 16 | 0 0  0  0 8 2 | * * * 1
```

```xx oo3xx3oo&#x   → height = 1
(ope || ope)

o. o.3o.3o.    | 12  * | 1  4  1 0  0 |  4 2 2 1  4  0 0 0 | 2 2 1  4 2 2 0 0 0 | 1 2 2 1 0
.o .o3.o3.o    |  * 12 | 0  0  1 1  4 |  0 0 0 1  4  4 2 2 | 0 0 0  4 2 2 2 2 1 | 0 2 2 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. .. .. ..    |  2  0 | 6  *  * *  * |  4 0 0 1  0  0 0 0 | 2 2 0  4 0 0 0 0 0 | 1 2 2 0 0
.. .. x. ..    |  2  0 | * 24  * *  * |  1 1 1 0  1  0 0 0 | 1 1 1  1 1 1 0 0 0 | 1 1 1 1 0
oo oo3oo3oo&#x |  1  1 | *  * 12 *  * |  0 0 0 1  4  0 0 0 | 0 0 0  4 2 2 0 0 0 | 0 2 2 1 0
.x .. .. ..    |  0  2 | *  *  * 6  * |  0 0 0 1  0  4 0 0 | 0 0 0  4 0 0 2 2 0 | 0 2 2 0 1
.. .. .x ..    |  0  2 | *  *  * * 24 |  0 0 0 0  1  1 1 1 | 0 0 0  1 1 1 1 1 1 | 0 1 1 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. .. x. ..    |  4  0 | 2  2  0 0  0 | 12 * * *  *  * * * | 1 1 0  1 0 0 0 0 0 | 1 1 1 0 0
.. o.3x. ..    |  3  0 | 0  3  0 0  0 |  * 8 * *  *  * * * | 1 0 1  0 1 0 0 0 0 | 1 1 0 1 0
.. .. x.3o.    |  3  0 | 0  3  0 0  0 |  * * 8 *  *  * * * | 0 1 1  0 0 1 0 0 0 | 1 0 1 1 0
xx .. .. ..&#x |  2  2 | 1  0  2 1  0 |  * * * 6  *  * * * | 0 0 0  4 0 0 0 0 0 | 0 2 2 0 0
.. .. xx ..&#x |  2  2 | 0  1  2 0  1 |  * * * * 24  * * * | 0 0 0  1 1 1 0 0 0 | 0 1 1 1 0
.x .. .x ..    |  0  4 | 0  0  0 2  2 |  * * * *  * 12 * * | 0 0 0  1 0 0 1 1 0 | 0 1 1 0 1
.. .o3.x ..    |  0  3 | 0  0  0 0  3 |  * * * *  *  * 8 * | 0 0 0  0 1 0 1 0 1 | 0 1 0 1 1
.. .. .x3.o    |  0  3 | 0  0  0 0  3 |  * * * *  *  * * 8 | 0 0 0  0 0 1 0 1 1 | 0 0 1 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. o.3x. ..    ♦  6  0 | 3  6  0 0  0 |  3 2 0 0  0  0 0 0 | 4 * *  * * * * * * | 1 1 0 0 0
x. .. x.3o.    ♦  6  0 | 3  6  0 0  0 |  3 0 2 0  0  0 0 0 | * 4 *  * * * * * * | 1 0 1 0 0
.. o.3x.3o.    ♦  6  0 | 0 12  0 0  0 |  0 4 4 0  0  0 0 0 | * * 2  * * * * * * | 1 0 0 1 0
xx .. xx ..&#x ♦  4  4 | 2  2  4 2  2 |  1 0 0 2  2  1 0 0 | * * * 12 * * * * * | 0 1 1 0 0
.. oo3xx ..&#x ♦  3  3 | 0  3  3 0  3 |  0 1 0 0  3  0 1 0 | * * *  * 8 * * * * | 0 1 0 1 0
.. .. xx3oo&#x ♦  3  3 | 0  3  3 0  3 |  0 0 1 0  3  0 0 1 | * * *  * * 8 * * * | 0 0 1 1 0
.x .o3.x ..    ♦  0  6 | 0  0  0 3  6 |  0 0 0 0  0  3 2 0 | * * *  * * * 4 * * | 0 1 0 0 1
.x .. .x3.o    ♦  0  6 | 0  0  0 3  6 |  0 0 0 0  0  3 0 2 | * * *  * * * * 4 * | 0 0 1 0 1
.. .o3.x3.o    ♦  0  6 | 0  0  0 0 12 |  0 0 0 0  0  0 4 4 | * * *  * * * * * 2 | 0 0 0 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. o.3x.3o.    ♦ 12  0 | 6 24  0 0  0 | 12 8 8 0  0  0 0 0 | 4 4 2  0 0 0 0 0 0 | 1 * * * *
xx oo3xx ..&#x ♦  6  6 | 3  6  6 3  6 |  3 2 0 3  6  3 2 0 | 1 0 0  3 2 0 1 0 0 | * 4 * * *
xx .. xx3oo&#x ♦  6  6 | 3  6  6 3  6 |  3 0 2 3  6  3 0 2 | 0 1 0  3 0 2 0 1 0 | * * 4 * *
.. oo3xx3oo&#x ♦  6  6 | 0 12  6 0 12 |  0 4 4 0 12  0 4 4 | 0 0 1  0 4 4 0 0 1 | * * * 2 *
.x .o3.x3.o    ♦  0 12 | 0  0  0 6 24 |  0 0 0 0  0 12 8 8 | 0 0 0  0 0 0 4 4 2 | * * * * 1
```

```xo3ox xx4oo&#x   → height = sqrt(2/3) = 0.816497
(tisdip || {3}-gyro tisdip)

o.3o. o.4o.    | 12  * |  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 .o4.o    |  * 12 |  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 | 12  *  *  *  * | 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 |  * 12  *  *  * | 0  2 1  0  0  2 0  0 0 | 1 2 0  2  1 2 0 0 | 1 2 2 1 0
oo3oo oo4oo&#x |  1  1 |  *  * 24  *  * | 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 |  *  *  * 12  * | 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 |  *  *  *  * 12 | 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 | 4  * *  *  *  * *  * * | 2 0 1  0  0 0 0 0 | 1 2 0 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 12 *  *  *  * *  * * | 1 1 0  1  0 0 0 0 | 1 1 1 0 0
.. .. x.4o.    |  4  0 |  0  4  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 | *  * * 12  *  * *  * * | 0 0 1  2  0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x |  1  2 |  0  0  2  1  0 | *  * *  * 12  * *  * * | 0 0 1  0  2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  *  * 24 *  * * | 0 0 0  1  1 1 0 0 | 0 1 1 1 0
.o3.x .. ..    |  0  3 |  0  0  0  3  0 | *  * *  *  *  * 4  * * | 0 0 1  0  0 0 2 0 | 0 2 0 0 1
.. .x .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  *  * * 12 * | 0 0 0  0  1 0 1 1 | 0 1 0 1 1
.. .. .x4.o    |  0  4 |  0  0  0  0  4 | *  * *  *  *  * *  * 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 | 4 * *  *  * * * * | 1 1 0 0 0
x. .. x.4o.    ♦  8  0 |  4  8  0  0  0 | 0  4 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 | * * 4  *  * * * * | 0 2 0 0 0
xo .. xx ..&#x ♦  4  2 |  2  2  4  0  1 | 0  1 0  2  0  2 0  0 0 | * * * 12  * * * * | 0 1 1 0 0
.. ox xx ..&#x ♦  2  4 |  0  1  4  2  2 | 0  0 0  0  2  2 0  1 0 | * * *  * 12 * * * | 0 1 0 1 0
.. .. xx4oo&#x ♦  4  4 |  0  4  4  0  4 | 0  0 1  0  0  4 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 | * * *  *  * * 4 * | 0 1 0 0 1
.. .x .x4.o    ♦  0  8 |  0  0  0  4  8 | 0  0 0  0  0  0 0  4 2 | * * *  *  * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.4o.    ♦ 12  0 | 12 12  0  0  0 | 4 12 3  0  0  0 0  0 0 | 4 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 | * 4 * * *
xo .. xx4oo&#x ♦  8  4 |  4  8  8  0  4 | 0  4 2  4  0  8 0  0 1 | 0 1 0  4  0 2 0 0 | * * 3 * *
.. ox xx4oo&#x ♦  4  8 |  0  4  8  4  8 | 0  0 1  0  4  8 0  4 2 | 0 0 0  0  4 2 0 1 | * * * 3 *
.o3.x .x4.o    ♦  0 12 |  0  0  0 12 12 | 0  0 0  0  0  0 4 12 3 | 0 0 0  0  0 0 4 3 | * * * * 1
```

```xx xx xo3ox&#x   → height = sqrt(2/3) = 0.816497
(tisdip || {3}-gyro tisdip)

o. o. o.3o.    | 12  * | 1 1  2  2 0 0  0 | 1 2 2 1  2  2  2  1 0 0 0 0 | 2 1 1 2 2 1 2 1 1 0 0 0 | 1 2 1 1 1 0
.o .o .o3.o    |  * 12 | 0 0  0  2 1 1  2 | 0 0 0 0  2  2  1  2 1 2 2 1 | 0 0 0 2 1 2 1 2 1 2 1 1 | 0 1 2 1 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. .. .. ..    |  2  0 | 6 *  *  * * *  * | 1 2 0 0  2  0  0  0 0 0 0 0 | 2 1 0 2 2 1 0 0 0 0 0 0 | 1 2 1 1 0 0
.. x. .. ..    |  2  0 | * 6  *  * * *  * | 1 0 2 0  0  2  0  0 0 0 0 0 | 2 0 1 2 0 0 2 1 0 0 0 0 | 1 2 1 0 1 0
.. .. x. ..    |  2  0 | * * 12  * * *  * | 0 1 1 1  0  0  1  0 0 0 0 0 | 1 1 1 0 1 0 1 0 1 0 0 0 | 1 1 0 1 1 0
oo oo oo3oo&#x |  1  1 | * *  * 24 * *  * | 0 0 0 0  1  1  1  1 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 | 0 1 1 1 1 0
.x .. .. ..    |  0  2 | * *  *  * 6 *  * | 0 0 0 0  2  0  0  0 1 2 0 0 | 0 0 0 2 1 2 0 0 0 2 1 0 | 0 1 2 1 0 1
.. .x .. ..    |  0  2 | * *  *  * * 6  * | 0 0 0 0  0  2  0  0 1 0 2 0 | 0 0 0 2 0 0 1 2 0 2 0 1 | 0 1 2 0 1 1
.. .. .. .x    |  0  2 | * *  *  * * * 12 | 0 0 0 0  0  0  0  1 0 1 1 1 | 0 0 0 0 0 1 0 1 1 1 1 1 | 0 0 1 1 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. x. .. ..    |  4  0 | 2 2  0  0 0 0  0 | 3 * * *  *  *  *  * * * * * | 2 0 0 2 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0
x. .. x. ..    |  4  0 | 2 0  2  0 0 0  0 | * 6 * *  *  *  *  * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
.. x. x. ..    |  4  0 | 0 2  2  0 0 0  0 | * * 6 *  *  *  *  * * * * * | 1 0 1 0 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0
.. .. x.3o.    |  3  0 | 0 0  3  0 0 0  0 | * * * 4  *  *  *  * * * * * | 0 1 1 0 0 0 0 0 1 0 0 0 | 1 0 0 1 1 0
xx .. .. ..&#x |  2  2 | 1 0  0  2 1 0  0 | * * * * 12  *  *  * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
.. xx .. ..&#x |  2  2 | 0 1  0  2 0 1  0 | * * * *  * 12  *  * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
.. .. xo ..&#x |  2  1 | 0 0  1  2 0 0  0 | * * * *  *  * 12  * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 | 0 1 0 1 1 0
.. .. .. ox&#x |  1  2 | 0 0  0  2 0 0  1 | * * * *  *  *  * 12 * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 1 1 0
.x .x .. ..    |  0  4 | 0 0  0  0 2 2  0 | * * * *  *  *  *  * 3 * * * | 0 0 0 2 0 0 0 0 0 2 0 0 | 0 1 2 0 0 1
.x .. .. .x    |  0  4 | 0 0  0  0 2 0  2 | * * * *  *  *  *  * * 6 * * | 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 1 1 0 1
.. .x .. .x    |  0  4 | 0 0  0  0 0 2  2 | * * * *  *  *  *  * * * 6 * | 0 0 0 0 0 0 0 1 0 1 0 1 | 0 0 1 0 1 1
.. .. .o3.x    |  0  3 | 0 0  0  0 0 0  3 | * * * *  *  *  *  * * * * 4 | 0 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. x. x. ..    ♦  8  0 | 4 4  4  0 0 0  0 | 2 2 2 0  0  0  0  0 0 0 0 0 | 3 * * * * * * * * * * * | 1 1 0 0 0 0
x. .. x.3o.    ♦  6  0 | 3 0  6  0 0 0  0 | 0 3 0 2  0  0  0  0 0 0 0 0 | * 2 * * * * * * * * * * | 1 0 0 1 0 0
.. x. x.3o.    ♦  6  0 | 0 3  6  0 0 0  0 | 0 0 3 2  0  0  0  0 0 0 0 0 | * * 2 * * * * * * * * * | 1 0 0 0 1 0
xx xx .. ..&#x ♦  4  4 | 2 2  0  4 2 2  0 | 1 0 0 0  2  2  0  0 1 0 0 0 | * * * 6 * * * * * * * * | 0 1 1 0 0 0
xx .. xo ..&#x ♦  4  2 | 2 0  2  4 1 0  0 | 0 1 0 0  2  0  2  0 0 0 0 0 | * * * * 6 * * * * * * * | 0 1 0 1 0 0
xx .. .. ox&#x ♦  2  4 | 1 0  0  4 2 0  2 | 0 0 0 0  2  0  0  2 0 1 0 0 | * * * * * 6 * * * * * * | 0 0 1 1 0 0
.. xx xo ..&#x ♦  4  2 | 0 2  2  4 0 1  0 | 0 0 1 0  0  2  2  0 0 0 0 0 | * * * * * * 6 * * * * * | 0 1 0 0 1 0
.. xx .. ox&#x ♦  2  4 | 0 1  0  4 0 2  2 | 0 0 0 0  0  2  0  2 0 0 1 0 | * * * * * * * 6 * * * * | 0 0 1 0 1 0
.. .. xo3ox&#x ♦  3  3 | 0 0  3  6 0 0  3 | 0 0 0 1  0  0  3  3 0 0 0 1 | * * * * * * * * 4 * * * | 0 0 0 1 1 0
.x .x .. .x    ♦  0  8 | 0 0  0  0 4 4  4 | 0 0 0 0  0  0  0  0 2 2 2 0 | * * * * * * * * * 3 * * | 0 0 1 0 0 1
.x .. .o3.x    ♦  0  6 | 0 0  0  0 3 0  6 | 0 0 0 0  0  0  0  0 0 3 0 2 | * * * * * * * * * * 2 * | 0 0 0 1 0 1
.. .x .o3.x    ♦  0  6 | 0 0  0  0 0 3  6 | 0 0 0 0  0  0  0  0 0 0 3 2 | * * * * * * * * * * * 2 | 0 0 0 0 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. x. x.3o.    ♦ 12  0 | 6 6 12  0 0 0  0 | 3 6 6 4  0  0  0  0 0 0 0 0 | 3 2 2 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xx xx xo ..&#x ♦  8  4 | 4 4  4  8 2 2  0 | 2 2 2 0  4  4  4  0 1 0 0 0 | 1 0 0 2 2 0 2 0 0 0 0 0 | * 3 * * * *
xx xx .. ox&#x ♦  4  8 | 2 2  0  8 4 4  4 | 1 0 0 0  4  4  0  4 2 2 2 0 | 0 0 0 2 0 2 0 2 0 1 0 0 | * * 3 * * *
xx .. xo3ox&#x ♦  6  6 | 3 0  6  6 3 0  6 | 0 3 0 2  6  0  6  6 0 3 0 2 | 0 1 0 0 3 3 0 0 2 0 1 0 | * * * 2 * *
.. xx xo3ox&#x ♦  6  6 | 0 3  6  6 0 3  6 | 0 0 3 2  0  6  6  6 0 0 3 2 | 0 0 1 0 0 0 3 3 2 0 0 1 | * * * * 2 *
.x .x .o3.x    ♦  0 12 | 0 0  0  0 6 6 12 | 0 0 0 0  0  0  0  0 3 6 6 4 | 0 0 0 0 0 0 0 0 0 3 2 2 | * * * * * 1
```

```oxo4ooo xxx4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107

o..4o.. o..4o..     | 4  * * | 2  4  0  0  0 0 | 1  4  8  0 0  0  0 0 | 1  8 4 0  0 0 | 2 4 0
.o.4.o. .o.4.o.     | * 16 * | 0  1  2  2  1 0 | 0  2  2  4 1  2  2 0 | 1  4 1 2  4 1 | 2 2 2
..o4..o ..o4..o     | *  * 4 | 0  0  0  0  4 2 | 0  0  0  0 0  4  8 1 | 1  0 0 0  8 4 | 2 0 4
--------------------+--------+-----------------+----------------------+---------------+------
... ... x.. ...     | 2  0 0 | 4  *  *  *  * * | 1  0  4  0 0  0  0 0 | 0  4 4 0  0 0 | 1 4 0
oo.4oo. oo.4oo.&#x  | 1  1 0 | * 16  *  *  * * | 0  2  2  0 0  0  0 0 | 1  4 1 0  0 0 | 2 2 0
.x. ... ... ...     | 0  2 0 | *  * 16  *  * * | 0  1  0  2 0  1  0 0 | 1  2 0 1  2 0 | 2 1 1
... ... .x. ...     | 0  2 0 | *  *  * 16  * * | 0  0  1  2 1  0  1 0 | 0  2 1 2  2 1 | 1 2 2
.oo4.oo .oo4.oo&#x  | 0  1 1 | *  *  *  * 16 * | 0  0  0  0 0  2  2 0 | 1  0 0 0  4 1 | 2 0 2
... ... ..x ...     | 0  0 2 | *  *  *  *  * 4 | 0  0  0  0 0  0  4 1 | 0  0 0 0  4 4 | 1 0 4
--------------------+--------+-----------------+----------------------+---------------+------
... ... x..4o..     | 4  0 0 | 4  0  0  0  0 0 | 1  *  *  * *  *  * * | 0  0 4 0  0 0 | 0 4 0
ox. ... ... ...&#x  | 1  2 0 | 0  2  1  0  0 0 | * 16  *  * *  *  * * | 1  2 0 0  0 0 | 2 1 0
... ... xx. ...&#x  | 2  2 0 | 1  2  0  1  0 0 | *  * 16  * *  *  * * | 0  2 1 0  0 0 | 1 2 0
.x. ... .x. ...     | 0  4 0 | 0  0  2  2  0 0 | *  *  * 16 *  *  * * | 0  1 0 1  1 0 | 1 1 1
... ... .x.4.o.     | 0  4 0 | 0  0  0  4  0 0 | *  *  *  * 4  *  * * | 0  0 1 2  0 1 | 0 2 2
.xo ... ... ...&#x  | 0  2 1 | 0  0  1  0  2 0 | *  *  *  * * 16  * * | 1  0 0 0  2 0 | 2 0 1
... ... .xx ...&#x  | 0  2 2 | 0  0  0  1  2 1 | *  *  *  * *  * 16 * | 0  0 0 0  2 1 | 1 0 2
... ... ..x4..o     | 0  0 4 | 0  0  0  0  0 4 | *  *  *  * *  *  * 1 | 0  0 0 0  0 4 | 0 0 4
--------------------+--------+-----------------+----------------------+---------------+------
oxo4ooo ... ...&#xt ♦ 1  4 1 | 0  4  4  0  4 0 | 0  4  0  0 0  4  0 0 | 4  * * *  * * | 2 0 0
ox. ... xx. ...&#x  ♦ 2  4 0 | 1  4  2  2  0 0 | 0  2  2  1 0  0  0 0 | * 16 * *  * * | 1 1 0
... ... xx.4oo.&#x  ♦ 4  4 0 | 4  4  0  4  0 0 | 1  0  4  0 1  0  0 0 | *  * 4 *  * * | 0 2 0
.x. ... .x.4.o.     ♦ 0  8 0 | 0  0  4  8  0 0 | 0  0  0  4 2  0  0 0 | *  * * 4  * * | 0 1 1
.xo ... .xx ...&#x  ♦ 0  4 2 | 0  0  2  2  4 1 | 0  0  0  1 0  2  2 0 | *  * * * 16 * | 1 0 1
... ... .xx4.oo&#x  ♦ 0  4 4 | 0  0  0  4  4 4 | 0  0  0  0 1  0  4 1 | *  * * *  * 4 | 0 0 2
--------------------+--------+-----------------+----------------------+---------------+------
oxo4ooo xxx ...&#xt ♦ 2  8 2 | 1  8  8  4  8 1 | 0  8  4  4 0  8  4 0 | 2  4 0 0  4 0 | 4 * *
ox. ... xx.4oo.&#x  ♦ 4  8 0 | 4  8  4  8  0 0 | 1  4  8  4 2  0  0 0 | 0  4 2 1  0 0 | * 4 *
.xo ... .xx4.oo&#x  ♦ 0  8 4 | 0  0  4  8  8 4 | 0  0  0  4 2  4  8 1 | 0  0 0 1  4 2 | * * 4
```
```or
o..4o.. o..4o..     & | 8  * | 2  4  0  0 | 1  4  8  0 0 | 1  8 4 0 | 2 4
.o.4.o. .o.4.o.       | * 16 | 0  2  2  2 | 0  4  4  4 1 | 1  8 2 2 | 2 4
----------------------+------+------------+--------------+----------+----
... ... x.. ...     & | 2  0 | 8  *  *  * | 1  0  4  0 0 | 0  4 4 0 | 1 4
oo.4oo. oo.4oo.&#x  & | 1  1 | * 32  *  * | 0  2  2  0 0 | 1  4 1 0 | 2 2
.x. ... ... ...       | 0  2 | *  * 16  * | 0  2  0  2 0 | 1  4 0 1 | 2 2
... ... .x. ...       | 0  2 | *  *  * 16 | 0  0  2  2 1 | 0  4 2 2 | 1 4
----------------------+------+------------+--------------+----------+----
... ... x..4o..     & | 4  0 | 4  0  0  0 | 2  *  *  * * | 0  0 4 0 | 0 4
ox. ... ... ...&#x  & | 1  2 | 0  2  1  0 | * 32  *  * * | 1  2 0 0 | 2 1
... ... xx. ...&#x  & | 2  2 | 1  2  0  1 | *  * 32  * * | 0  2 1 0 | 1 2
.x. ... .x. ...       | 0  4 | 0  0  2  2 | *  *  * 16 * | 0  2 0 1 | 1 2
... ... .x.4.o.       | 0  4 | 0  0  0  4 | *  *  *  * 4 | 0  0 2 2 | 0 4
----------------------+------+------------+--------------+----------+----
oxo4ooo ... ...&#xt   ♦ 2  4 | 0  8  4  0 | 0  8  0  0 0 | 4  * * * | 2 0
ox. ... xx. ...&#x  & ♦ 2  4 | 1  4  2  2 | 0  2  2  1 0 | * 32 * * | 1 1
... ... xx.4oo.&#x  & ♦ 4  4 | 4  4  0  4 | 1  0  4  0 1 | *  * 8 * | 0 2
.x. ... .x.4.o.       ♦ 0  8 | 0  0  4  8 | 0  0  0  4 2 | *  * * 4 | 0 2
----------------------+------+------------+--------------+----------+----
oxo4ooo xxx ...&#xt   ♦ 4  8 | 2 16  8  4 | 0 16  8  4 0 | 2  8 0 0 | 4 *
ox. ... xx.4oo.&#x  & ♦ 4  8 | 4  8  4  8 | 1  4  8  4 2 | 0  4 2 1 | * 8
```

```qo ox4oo xx4oo&#zx   → height = 0
(tegum sum of q x4o and ortho base-para tes)

o. o.4o. o.4o.     | 8  * | 2  4  0  0 | 1  4  8  0 0 | 1  8 4 0 | 2 4
.o .o4.o .o4.o     | * 16 | 0  2  2  2 | 0  4  4  4 1 | 1  8 2 2 | 2 4
-------------------+------+------------+--------------+----------+----
.. .. .. x. ..     | 2  0 | 8  *  *  * | 1  0  4  0 0 | 0  4 4 0 | 1 4
oo oo4oo oo4oo&#x  | 1  1 | * 32  *  * | 0  2  2  0 0 | 1  4 1 0 | 2 2
.. .x .. .. ..     | 0  2 | *  * 16  * | 0  2  0  2 0 | 1  4 0 1 | 2 2
.. .. .. .x ..     | 0  2 | *  *  * 16 | 0  0  2  2 1 | 0  4 2 2 | 1 4
-------------------+------+------------+--------------+----------+----
.. .. .. x.4o.     | 4  0 | 4  0  0  0 | 2  *  *  * * | 0  0 4 0 | 0 4
.. ox .. .. ..&#x  | 1  2 | 0  2  1  0 | * 32  *  * * | 1  2 0 0 | 2 1
.. .. .. xx ..&#x  | 2  2 | 1  2  0  1 | *  * 32  * * | 0  2 1 0 | 1 2
.. .x .. .x ..     | 0  4 | 0  0  2  2 | *  *  * 16 * | 0  2 0 1 | 1 2
.. .. .. .x4.o     | 0  4 | 0  0  0  4 | *  *  *  * 4 | 0  0 2 2 | 0 4
-------------------+------+------------+--------------+----------+----
qo ox4oo .. ..&#zx ♦ 2  4 | 0  8  4  0 | 0  8  0  0 0 | 4  * * * | 2 0
.. ox .. xx ..&#x  ♦ 2  4 | 1  4  2  2 | 0  2  2  1 0 | * 32 * * | 1 1
.. .. .. xx4oo&#x  ♦ 4  4 | 4  4  0  4 | 1  0  4  0 1 | *  * 8 * | 0 2
.. .x .. .x4.o     ♦ 0  8 | 0  0  4  8 | 0  0  0  4 2 | *  * * 4 | 0 2
-------------------+------+------------+--------------+----------+----
qo ox4oo xx ..&#zx ♦ 4  8 | 2 16  8  4 | 0 16  8  4 0 | 2  8 0 0 | 4 *
.. ox .. xx4oo&#x  ♦ 4  8 | 4  8  4  8 | 1  4  8  4 2 | 0  4 2 1 | * 8
```