Acronym teta ope (alt.: octarap, tetoct octtric) Name tetrahedron atop octahedron-prism,octahedron atop rectified-pentachoron,half of dodecateron (its tet-first rotunda),(tet,oct,oct)-trigonic Circumradius sqrt(3)/2 = 0.866025 Lace cityin approx. ASCII-art ```O t where: t = x3o3o (tet) O O = o3x3o (oct) ``` Confer uniform relative: dot   related segmentotera: taope   general polytopal classes: segmentotera   lace simplices

Incidence matrix according to Dynkin symbol

```ox xo3ox3oo&#x   → height = sqrt(3/8) = 0.612372
(tet || ope)

o. o.3o.3o.    | 4  * ♦ 3  6 0  0 | 3  3  6  6  0 0 0 | 1 3  3 6 2 0 0 0 | 3 1 2 0
.o .o3.o3.o    | * 12 | 0  2 1  4 | 0  2  1  4  4 2 2 | 0 1  4 2 2 2 2 1 | 2 2 1 1
---------------+------+-----------+-------------------+------------------+--------
.. x. .. ..    | 2  0 | 6  * *  * | 2  0  2  0  0 0 0 | 1 1  0 4 0 0 0 0 | 2 0 2 0
oo oo3oo3oo&#x | 1  1 | * 24 *  * | 0  1  1  2  0 0 0 | 0 1  2 2 1 0 0 0 | 2 1 1 0
.x .. .. ..    | 0  2 | *  * 6  * | 0  2  0  0  4 0 0 | 0 1  4 0 0 2 2 0 | 2 2 0 1
.. .. .x ..    | 0  2 | *  * * 24 | 0  0  0  1  1 1 1 | 0 0  1 1 1 1 1 1 | 1 1 1 1
---------------+------+-----------+-------------------+------------------+--------
.. x.3o. ..    | 3  0 | 3  0 0  0 | 4  *  *  *  * * * | 1 0  0 2 0 0 0 0 | 1 0 2 0
ox .. .. ..&#x | 1  2 | 0  2 1  0 | * 12  *  *  * * * | 0 1  2 0 0 0 0 0 | 2 1 0 0
.. xo .. ..&#x | 2  1 | 1  2 0  0 | *  * 12  *  * * * | 0 1  0 2 0 0 0 0 | 2 0 1 0
.. .. ox ..&#x | 1  2 | 0  2 0  1 | *  *  * 24  * * * | 0 0  1 1 1 0 0 0 | 1 1 1 0
.x .. .x ..    | 0  4 | 0  0 2  2 | *  *  *  * 12 * * | 0 0  1 0 0 1 1 0 | 1 1 0 1
.. .o3.x ..    | 0  3 | 0  0 0  3 | *  *  *  *  * 8 * | 0 0  0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.o    | 0  3 | 0  0 0  3 | *  *  *  *  * * 8 | 0 0  0 0 1 0 1 1 | 0 1 1 1
---------------+------+-----------+-------------------+------------------+--------
.. x.3o.3o.    ♦ 4  0 | 6  0 0  0 | 4  0  0  0  0 0 0 | 1 *  * * * * * * | 0 0 2 0
ox xo .. ..&#x ♦ 2  2 | 1  4 1  0 | 0  2  2  0  0 0 0 | * 6  * * * * * * | 2 0 0 0
ox .. ox ..&#x ♦ 1  4 | 0  4 2  2 | 0  2  0  2  1 0 0 | * * 12 * * * * * | 1 1 0 0
.. xo3ox ..&#x ♦ 3  3 | 3  6 0  3 | 1  0  3  3  0 1 0 | * *  * 8 * * * * | 1 0 1 0
.. .. ox3oo&#x ♦ 1  3 | 0  3 0  3 | 0  0  0  3  0 0 1 | * *  * * 8 * * * | 0 1 1 0
.x .o3.x ..    ♦ 0  6 | 0  0 3  6 | 0  0  0  0  3 2 0 | * *  * * * 4 * * | 1 0 0 1
.x .. .x3.o    ♦ 0  6 | 0  0 3  6 | 0  0  0  0  3 0 2 | * *  * * * * 4 * | 0 1 0 1
.. .o3.x3.o    ♦ 0  6 | 0  0 0 12 | 0  0  0  0  0 4 4 | * *  * * * * * 2 | 0 0 1 1
---------------+------+-----------+-------------------+------------------+--------
ox xo3ox ..&#x ♦ 3  6 | 3 12 3  6 | 1  6  6  6  3 2 0 | 0 3  3 2 0 1 0 0 | 4 * * *
ox .. ox3oo&#x ♦ 1  6 | 0  6 3  6 | 0  3  0  6  3 0 2 | 0 0  3 0 2 0 1 0 | * 4 * *
.. xo3ox3oo&#x ♦ 4  6 | 6 12 0 12 | 4  0  6 12  0 4 4 | 1 0  0 4 4 0 0 1 | * * 2 *
.x .o3.x3.o    ♦ 0 12 | 0  0 6 24 | 0  0  0  0 12 8 8 | 0 0  0 0 0 4 4 2 | * * * 1
```

```ooo3oxx3xoo&#x   → height(1,2) = height(1,3) = sqrt(5/8) = 0.790569
height(2,3) = 1
height(1,23) = sqrt(3/8) = 0.612372

o..3o..3o..    | 4 * * | 3  3  3  0 0  0 | 3  3 3  3  3 3 0 0  0 0 0 | 1 1 3  3 3 1 3 0 0 0 0 | 1 1 3 1 0
.o.3.o.3.o.    | * 6 * | 0  2  0  4 1  0 | 0  4 1  2  0 0 2 2  4 0 0 | 0 2 2  4 1 0 0 1 2 2 0 | 1 2 2 0 1
..o3..o3..o    | * * 6 | 0  0  2  0 1  4 | 0  0 0  2  4 1 0 0  4 2 2 | 0 0 0  4 1 2 2 0 2 2 1 | 0 2 2 1 1
---------------+-------+-----------------+---------------------------+------------------------+----------
... ... x..    | 2 0 0 | 6  *  *  * *  * | 2  0 1  0  0 1 0 0  0 0 0 | 1 0 2  0 1 0 2 0 0 0 0 | 1 0 2 1 0
oo.3oo.3oo.&#x | 1 1 0 | * 12  *  * *  * | 0  2 1  1  0 0 0 0  0 0 0 | 0 1 2  2 1 0 0 0 0 0 0 | 1 1 2 0 0
o.o3o.o3o.o&#x | 1 0 1 | *  * 12  * *  * | 0  0 0  1  2 2 0 0  0 0 0 | 0 0 0  2 1 1 2 0 0 0 0 | 0 1 2 1 0
... .x. ...    | 0 2 0 | *  *  * 12 *  * | 0  1 0  0  0 0 1 1  1 0 0 | 0 1 1  1 0 0 0 1 1 1 0 | 1 1 1 0 1
.oo3.oo3.oo&#x | 0 1 1 | *  *  *  * 6  * | 0  0 0  2  0 0 0 0  4 0 0 | 0 0 0  4 1 0 0 0 2 2 0 | 0 2 2 0 1
... ..x ...    | 0 0 2 | *  *  *  * * 12 | 0  0 0  0  1 0 0 0  1 1 1 | 0 0 0  1 0 1 1 0 1 1 1 | 0 1 1 1 1
---------------+-------+-----------------+---------------------------+------------------------+----------
... o..3x..    | 3 0 0 | 3  0  0  0 0  0 | 4  * *  *  * * * *  * * * | 1 0 1  0 0 0 1 0 0 0 0 | 1 0 1 1 0
... ox. ...&#x | 1 2 0 | 0  2  0  1 0  0 | * 12 *  *  * * * *  * * * | 0 1 1  1 0 0 0 0 0 0 0 | 1 1 1 0 0
... ... xo.&#x | 2 1 0 | 1  2  0  0 0  0 | *  * 6  *  * * * *  * * * | 0 0 2  0 1 0 0 0 0 0 0 | 1 0 2 0 0
ooo3ooo3ooo&#x | 1 1 1 | 0  1  1  0 1  0 | *  * * 12  * * * *  * * * | 0 0 0  2 1 0 0 0 0 0 0 | 0 1 2 0 0
... o.x ...&#x | 1 0 2 | 0  0  2  0 0  1 | *  * *  * 12 * * *  * * * | 0 0 0  1 0 1 1 0 0 0 0 | 0 1 1 1 0
... ... x.o&#x | 2 0 1 | 1  0  2  0 0  0 | *  * *  *  * 6 * *  * * * | 0 0 0  0 1 0 2 0 0 0 0 | 0 0 2 1 0
.o.3.x. ...    | 0 3 0 | 0  0  0  3 0  0 | *  * *  *  * * 4 *  * * * | 0 1 0  0 0 0 0 1 1 0 0 | 1 1 0 0 1
... .x.3.o.    | 0 3 0 | 0  0  0  3 0  0 | *  * *  *  * * * 4  * * * | 0 0 1  0 0 0 0 1 0 1 0 | 1 0 1 0 1
... .xx ...&#x | 0 2 2 | 0  0  0  1 2  1 | *  * *  *  * * * * 12 * * | 0 0 0  1 0 0 0 0 1 1 0 | 0 1 1 0 1
..o3..x ...    | 0 0 3 | 0  0  0  0 0  3 | *  * *  *  * * * *  * 4 * | 0 0 0  0 0 1 0 0 1 0 1 | 0 1 0 1 1
... ..x3..o    | 0 0 3 | 0  0  0  0 0  3 | *  * *  *  * * * *  * * 4 | 0 0 0  0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+-------+-----------------+---------------------------+------------------------+----------
o..3o..3x..    ♦ 4 0 0 | 6  0  0  0 0  0 | 4  0 0  0  0 0 0 0  0 0 0 | 1 * *  * * * * * * * * | 1 0 0 1 0
oo.3ox. ...&#x ♦ 1 3 0 | 0  3  0  3 0  0 | 0  3 0  0  0 0 1 0  0 0 0 | * 4 *  * * * * * * * * | 1 1 0 0 0
... ox.3xo.&#x ♦ 3 3 0 | 3  6  0  3 0  0 | 1  3 3  0  0 0 0 1  0 0 0 | * * 4  * * * * * * * * | 1 0 1 0 0
... oxx ...&#x ♦ 1 2 2 | 0  2  2  1 2  1 | 0  1 0  2  1 0 0 0  1 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0
... ... xoo&#x ♦ 2 1 1 | 1  2  2  0 1  0 | 0  0 1  2  0 1 0 0  0 0 0 | * * *  * 6 * * * * * * | 0 0 2 0 0
o.o3o.x ...&#x ♦ 1 0 3 | 0  0  3  0 0  3 | 0  0 0  0  3 0 0 0  0 1 0 | * * *  * * 4 * * * * * | 0 1 0 1 0
... o.x3x.o&#x ♦ 3 0 3 | 3  0  6  0 0  3 | 1  0 0  0  3 3 0 0  0 0 1 | * * *  * * * 4 * * * * | 0 0 1 1 0
.o.3.x.3.o.    ♦ 0 6 0 | 0  0  0 12 0  0 | 0  0 0  0  0 0 4 4  0 0 0 | * * *  * * * * 1 * * * | 1 0 0 0 1
.oo3.xx ...&#x ♦ 0 3 3 | 0  0  0  3 3  3 | 0  0 0  0  0 0 1 0  3 1 0 | * * *  * * * * * 4 * * | 0 1 0 0 1
... .xx3.oo&#x ♦ 0 3 3 | 0  0  0  3 3  3 | 0  0 0  0  0 0 0 1  3 0 1 | * * *  * * * * * * 4 * | 0 0 1 0 1
..o3..x3..o    ♦ 0 0 6 | 0  0  0  0 0 12 | 0  0 0  0  0 0 0 0  0 4 4 | * * *  * * * * * * * 1 | 0 0 0 1 1
---------------+-------+-----------------+---------------------------+------------------------+----------
oo.3ox.3xo.&#x ♦ 4 6 0 | 6 12  0 12 0  0 | 4 12 6  0  0 0 4 4  0 0 0 | 1 4 4  0 0 0 0 1 0 0 0 | 1 * * * *
ooo3oxx ...&#x ♦ 1 3 3 | 0  3  3  3 3  3 | 0  3 0  3  3 0 1 0  3 1 0 | 0 1 0  3 0 1 0 0 1 0 0 | * 4 * * *
... oxx3xoo&#x ♦ 3 3 3 | 3  6  6  3 3  3 | 1  3 3  6  3 3 0 1  3 0 1 | 0 0 1  3 3 0 1 0 0 1 0 | * * 4 * *
o.o3o.x3x.o&#x ♦ 4 0 6 | 6  0 12  0 0 12 | 4  0 0  0 12 6 0 0  0 4 4 | 1 0 0  0 0 4 4 0 0 0 1 | * * * 1 *
.oo3.xx3.oo&#x ♦ 0 6 6 | 0  0  0 12 6 12 | 0  0 0  0  0 0 4 4 12 4 4 | 0 0 0  0 0 0 0 1 4 4 1 | * * * * 1
```

```o3x3o || oo3ox3xo&#x   → height = sqrt(3/5) = 0.774597
(oct || rap)

o3o3o   .. .. ..    | 6 * * |  4  2 1 0  0  0 | 2 2 1  4  2  4 0  0 0 0 0 | 1 2 2  4 1 2 2 0 0 0 0 | 1 2 2 1 0
. . .   o.3o.3o.    | * 4 * |  0  3 0 3  3  0 | 0 0 3  3  3  0 3  3 3 0 0 | 0 1 3  3 3 0 0 1 1 3 0 | 1 1 3 0 1
. . .   .o3.o3.o    | * * 6 |  0  0 1 0  2  4 | 0 0 0  0  2  4 0  4 1 2 2 | 0 0 0  4 1 2 2 0 2 2 1 | 0 2 2 1 1
--------------------+-------+-----------------+---------------------------+------------------------+----------
. x .   .. .. ..    | 2 0 0 | 12  * * *  *  * | 1 1 0  1  0  1 0  0 0 0 0 | 1 1 1  1 0 1 1 0 0 0 0 | 1 1 1 1 0
o3o3o || o.3o.3o.    | 1 1 0 |  * 12 * *  *  * | 0 0 1  2  1  0 0  0 0 0 0 | 0 1 2  2 1 0 0 0 0 0 0 | 1 1 2 0 0
o3o3o || .o3.o3.o    | 1 0 1 |  *  * 6 *  *  * | 0 0 0  0  2  4 0  0 0 0 0 | 0 0 0  4 1 2 2 0 0 0 0 | 0 2 2 1 0
. . .   .. .. x.    | 0 2 0 |  *  * * 6  *  * | 0 0 1  0  0  0 2  0 1 0 0 | 0 0 2  0 1 0 0 1 0 2 0 | 1 0 2 0 1
. . .   oo3oo3oo&#x | 0 1 1 |  *  * * * 12  * | 0 0 0  0  1  0 0  2 1 0 0 | 0 0 0  2 1 0 0 0 1 2 0 | 0 1 2 0 1
. . .   .. .x ..    | 0 0 2 |  *  * * *  * 12 | 0 0 0  0  0  1 0  1 0 1 1 | 0 0 0  1 0 1 1 0 1 1 1 | 0 1 1 1 1
--------------------+-------+-----------------+---------------------------+------------------------+----------
o3x .   .. .. ..    | 3 0 0 |  3  0 0 0  0  0 | 4 * *  *  *  * *  * * * * | 1 1 0  0 0 1 0 0 0 0 0 | 1 1 0 1 0
. x3o   .. .. ..    | 3 0 0 |  3  0 0 0  0  0 | * 4 *  *  *  * *  * * * * | 1 0 1  0 0 0 1 0 0 0 0 | 1 0 1 1 0
o3o3o || .. .. x.    | 1 2 0 |  0  2 0 1  0  0 | * * 6  *  *  * *  * * * * | 0 0 2  0 1 0 0 0 0 0 0 | 1 0 2 0 0
. x . || o.3o.3o.    | 2 1 0 |  1  2 0 0  0  0 | * * * 12  *  * *  * * * * | 0 1 1  1 0 0 0 0 0 0 0 | 1 1 1 0 0
o3o3o || oo3oo3oo&#x | 1 1 1 |  0  1 1 0  1  0 | * * *  * 12  * *  * * * * | 0 0 0  2 1 0 0 0 0 0 0 | 0 1 2 0 0
. x . || .. .x ..    | 2 0 2 |  1  0 2 0  0  1 | * * *  *  * 12 *  * * * * | 0 0 0  1 0 1 1 0 0 0 0 | 0 1 1 1 0
. . .   .. o.3x.    | 0 3 0 |  0  0 0 3  0  0 | * * *  *  *  * 4  * * * * | 0 0 1  0 0 0 0 1 0 1 0 | 1 0 1 0 1
. . .   .. ox ..&#x | 0 1 2 |  0  0 0 0  2  1 | * * *  *  *  * * 12 * * * | 0 0 0  1 0 0 0 0 1 1 0 | 0 1 1 0 1
. . .   .. .. xo&#x | 0 2 1 |  0  0 0 1  2  0 | * * *  *  *  * *  * 6 * * | 0 0 0  0 1 0 0 0 0 2 0 | 0 0 2 0 1
. . .   .o3.x ..    | 0 0 3 |  0  0 0 0  0  3 | * * *  *  *  * *  * * 4 * | 0 0 0  0 0 1 0 0 1 0 1 | 0 1 0 1 1
. . .   .. .x3.o    | 0 0 3 |  0  0 0 0  0  3 | * * *  *  *  * *  * * * 4 | 0 0 0  0 0 0 1 0 0 1 1 | 0 0 1 1 1
--------------------+-------+-----------------+---------------------------+------------------------+----------
o3x3o   .. .. ..    ♦ 6 0 0 | 12  0 0 0  0  0 | 4 4 0  0  0  0 0  0 0 0 0 | 1 * *  * * * * * * * * | 1 0 0 1 0
o3x . || o.3o. ..    ♦ 3 1 0 |  3  3 0 0  0  0 | 1 0 0  3  0  0 0  0 0 0 0 | * 4 *  * * * * * * * * | 1 1 0 0 0
. x3o || .. o.3x.    ♦ 3 3 0 |  3  6 0 3  0  0 | 0 1 3  3  0  0 1  0 0 0 0 | * * 4  * * * * * * * * | 1 0 1 0 0
. x . || .. ox ..&#x ♦ 2 1 2 |  1  2 2 0  2  1 | 0 0 0  1  2  1 0  1 0 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0
o3o3o || .. .. xo&#x ♦ 1 2 1 |  0  2 1 1  2  0 | 0 0 1  0  2  0 0  0 1 0 0 | * * *  * 6 * * * * * * | 0 0 2 0 0
o3x . || .o3.x ..    ♦ 3 0 3 |  3  0 3 0  0  3 | 1 0 0  0  0  3 0  0 0 1 0 | * * *  * * 4 * * * * * | 0 1 0 1 0
. x3o || .. .x3.o    ♦ 3 0 3 |  3  0 3 0  0  3 | 0 1 0  0  0  3 0  0 0 0 1 | * * *  * * * 4 * * * * | 0 0 1 1 0
. . .   o.3o.3x.    ♦ 0 4 0 |  0  0 0 6  0  0 | 0 0 0  0  0  0 4  0 0 0 0 | * * *  * * * * 1 * * * | 1 0 0 0 1
. . .   oo3ox ..&#x ♦ 0 1 3 |  0  0 0 0  3  3 | 0 0 0  0  0  0 0  3 0 1 0 | * * *  * * * * * 4 * * | 0 1 0 0 1
. . .   .. ox3xo&#x ♦ 0 3 3 |  0  0 0 3  6  3 | 0 0 0  0  0  0 1  3 3 0 1 | * * *  * * * * * * 4 * | 0 0 1 0 1
. . .   .o3.x3.o    ♦ 0 0 6 |  0  0 0 0  0 12 | 0 0 0  0  0  0 0  0 0 4 4 | * * *  * * * * * * * 1 | 0 0 0 1 1
--------------------+-------+-----------------+---------------------------+------------------------+----------
o3x3o || o.3o.3x.    ♦ 6 4 0 | 12 12 0 6  0  0 | 4 4 6 12  0  0 4  0 0 0 0 | 1 4 4  0 0 0 0 1 0 0 0 | 1 * * * *
o3x . || oo3ox ..&#x ♦ 3 1 3 |  3  3 3 0  3  3 | 1 0 0  3  3  3 0  3 0 1 0 | 0 1 0  3 0 1 0 0 1 0 0 | * 4 * * *
. x3o || .. ox3xo&#x ♦ 3 3 3 |  3  6 3 3  6  3 | 0 1 3  3  6  3 1  3 3 0 1 | 0 0 1  3 3 0 1 0 0 1 0 | * * 4 * *
o3x3o || o.3.x3.o    ♦ 6 0 6 | 12  0 6 0  0 12 | 4 4 0  0  0 12 0  0 0 4 4 | 1 0 0  0 0 4 4 0 0 0 1 | * * * 1 *
. . .   oo3ox3xo&#x ♦ 0 4 6 |  0  0 0 6 12 12 | 0 0 0  0  0  0 4 12 6 4 4 | 0 0 0  0 0 0 0 1 4 4 1 | * * * * 1
```

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