Acronym tratet altroct
Name triangle-tetrahedron duoprism atop gyrated triangle-octahedron duoprism,
vertex-first medial segment of birectified heptapeton
Circumradius sqrt(6/7) = 0.925820
Lace city
in approx. ASCII-art
      +---- x3o x3o3o (tratet)
     /  +-- o3x o3x3o (gyro troct)
    /  /

  T  o
      
t  O  

where:
T = x x3o3o (tepe)
o = o o3x3o (oct)
t = o x3o3o (tet)
O = x o3x3o (ope)
Confer
uniform relative:
bril  
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

xo3ox xo3ox3oo&#x   → height = sqrt(7/24) = 0.540062
(tratet || gyro troct)

o.3o. o.3o.3o.    | 12  * |  2  3  6  0  0 | 1  6  3  6  3  6  6 0  0  0  0 | 3  6 1  3  6  6  3  3  6  2  0  0  0 0 | 3 1 3  3  6  2  3  1 2 0 0 0 | 1 3 1 2 1 0
.o3.o .o3.o3.o    |  * 18 |  0  0  4  2  4 | 0  0  0  2  4  2  8 1  8  2  2 | 0  0 0  2  1  4  2  8  4  4  4  4  4 1 | 0 0 1  4  2  2  4  4 2 2 2 2 | 0 2 2 1 2 1
------------------+-------+----------------+--------------------------------+----------------------------------------+------------------------------+------------
x. .. .. .. ..    |  2  0 | 12  *  *  *  * | 1  3  0  3  0  0  0 0  0  0  0 | 3  3 0  3  3  3  0  0  0  0  0  0  0 0 | 3 1 3  3  3  1  0  0 2 0 0 0 | 1 3 1 1 0 0
.. .. x. .. ..    |  2  0 |  * 18  *  *  * | 0  2  2  0  0  2  0 0  0  0  0 | 1  4 1  0  2  0  1  0  4  0  0  0  0 0 | 2 2 1  0  4  0  2  0 2 0 0 0 | 1 2 0 2 1 0
oo3oo oo3oo3oo&#x |  1  1 |  *  * 72  *  * | 0  0  0  1  1  1  2 0  0  0  0 | 0  0 0  1  1  2  1  2  2  1  0  0  0 0 | 0 0 1  2  2  1  2  1 1 0 0 0 | 0 2 1 1 1 0
.. .x .. .. ..    |  0  2 |  *  *  * 18  * | 0  0  0  0  2  0  0 1  4  0  0 | 0  0 0  2  0  0  1  4  0  0  4  2  2 0 | 0 0 1  4  0  0  2  2 0 2 2 1 | 0 2 2 0 1 1
.. .. .. .x ..    |  0  2 |  *  *  *  * 36 | 0  0  0  0  0  0  2 0  2  1  1 | 0  0 0  0  0  1  0  2  2  2  1  2  2 1 | 0 0 0  1  1  1  2  2 2 1 1 2 | 0 1 1 1 2 1
------------------+-------+----------------+--------------------------------+----------------------------------------+------------------------------+------------
x.3o. .. .. ..    |  3  0 |  3  0  0  0  0 | 4  *  *  *  *  *  * *  *  *  * | 3  0 0  3  0  0  0  0  0  0  0  0  0 0 | 3 0 3  3  0  0  0  0 0 0 0 0 | 1 3 1 0 0 0
x. .. x. .. ..    |  4  0 |  2  2  0  0  0 | * 18  *  *  *  *  * *  *  *  * | 1  2 0  0  1  0  0  0  0  0  0  0  0 0 | 2 1 1  0  2  0  0  0 0 0 0 0 | 1 2 0 1 0 0
.. .. x.3o. ..    |  3  0 |  0  3  0  0  0 | *  * 12  *  *  *  * *  *  *  * | 0  2 1  0  0  0  0  0  2  0  0  0  0 0 | 1 2 0  0  2  0  1  0 2 0 0 0 | 1 1 0 2 1 0
xo .. .. .. ..&#x |  2  1 |  1  0  2  0  0 | *  *  * 36  *  *  * *  *  *  * | 0  0 0  1  1  2  0  0  0  0  0  0  0 0 | 0 0 1  2  2  1  0  0 0 0 0 0 | 0 2 1 1 0 0
.. ox .. .. ..&#x |  1  2 |  0  0  2  1  0 | *  *  *  * 36  *  * *  *  *  * | 0  0 0  1  0  0  1  2  0  0  0  0  0 0 | 0 0 1  2  0  0  2  1 0 0 0 0 | 0 2 1 0 1 0
.. .. xo .. ..&#x |  2  1 |  0  1  2  0  0 | *  *  *  *  * 36  * *  *  *  * | 0  0 0  0  1  0  1  0  2  0  0  0  0 0 | 0 0 1  0  2  0  2  0 1 0 0 0 | 0 2 0 1 1 0
.. .. .. ox ..&#x |  1  2 |  0  0  2  0  1 | *  *  *  *  *  * 72 *  *  *  * | 0  0 0  0  0  1  0  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
.o3.x .. .. ..    |  0  3 |  0  0  0  3  0 | *  *  *  *  *  *  * 6  *  *  * | 0  0 0  2  0  0  0  0  0  0  4  0  0 0 | 0 0 1  4  0  0  0  0 0 2 2 0 | 0 2 2 0 0 1
.. .x .. .x ..    |  0  4 |  0  0  0  2  2 | *  *  *  *  *  *  * * 36  *  * | 0  0 0  0  0  0  0  1  0  0  1  1  1 0 | 0 0 0  1  0  0  1  1 0 1 1 1 | 0 1 1 0 1 1
.. .. .o3.x ..    |  0  3 |  0  0  0  0  3 | *  *  *  *  *  *  * *  * 12  * | 0  0 0  0  0  0  0  0  2  0  0  2  0 1 | 0 0 0  0  1  0  2  0 2 1 0 2 | 0 1 0 1 2 1
.. .. .. .x3.o    |  0  3 |  0  0  0  0  3 | *  *  *  *  *  *  * *  *  * 12 | 0  0 0  0  0  0  0  0  0  2  0  0  2 1 | 0 0 0  0  0  1  0  2 2 0 1 2 | 0 0 1 1 2 1
------------------+-------+----------------+--------------------------------+----------------------------------------+------------------------------+------------
x.3o. x. .. ..      6  0 |  6  3  0  0  0 | 2  3  0  0  0  0  0 0  0  0  0 | 6  * *  *  *  *  *  *  *  *  *  *  * * | 2 0 1  0  0  0  0  0 0 0 0 0 | 1 2 0 0 0 0
x. .. x.3o. ..      6  0 |  3  6  0  0  0 | 0  3  2  0  0  0  0 0  0  0  0 | * 12 *  *  *  *  *  *  *  *  *  *  * * | 1 1 0  0  1  0  0  0 0 0 0 0 | 1 1 0 1 0 0
.. .. x.3o.3o.      4  0 |  0  6  0  0  0 | 0  0  4  0  0  0  0 0  0  0  0 | *  * 3  *  *  *  *  *  *  *  *  *  * * | 0 2 0  0  0  0  0  0 2 0 0 0 | 1 0 0 2 1 0
xo3ox .. .. ..&#x   3  3 |  3  0  6  3  0 | 1  0  0  3  3  0  0 1  0  0  0 | *  * * 12  *  *  *  *  *  *  *  *  * * | 0 0 1  2  0  0  0  0 0 0 0 0 | 0 2 1 0 0 0
xo .. xo .. ..&#x   4  1 |  2  2  4  0  0 | 0  1  0  2  0  2  0 0  0  0  0 | *  * *  * 18  *  *  *  *  *  *  *  * * | 0 0 1  0  2  0  0  0 0 0 0 0 | 0 2 0 1 0 0
xo .. .. ox ..&#x   2  2 |  1  0  4  0  1 | 0  0  0  2  0  0  2 0  0  0  0 | *  * *  *  * 36  *  *  *  *  *  *  * * | 0 0 0  1  1  1  0  0 0 0 0 0 | 0 1 1 1 0 0
.. ox xo .. ..&#x   2  2 |  0  1  4  1  0 | 0  0  0  0  2  2  0 0  0  0  0 | *  * *  *  *  * 18  *  *  *  *  *  * * | 0 0 1  0  0  0  2  0 0 0 0 0 | 0 2 0 0 1 0
.. ox .. ox ..&#x   1  4 |  0  0  4  2  2 | 0  0  0  0  2  0  2 0  1  0  0 | *  * *  *  *  *  * 36  *  *  *  *  * * | 0 0 0  1  0  0  1  1 0 0 0 0 | 0 1 1 0 1 0
.. .. xo3ox ..&#x   3  3 |  0  3  6  0  3 | 0  0  1  0  0  3  3 0  0  1  0 | *  * *  *  *  *  *  * 24  *  *  *  * * | 0 0 0  0  1  0  1  0 1 0 0 0 | 0 1 0 1 1 0
.. .. .. ox3oo&#x   1  3 |  0  0  3  0  3 | 0  0  0  0  0  0  3 0  0  0  1 | *  * *  *  *  *  *  *  * 24  *  *  * * | 0 0 0  0  0  1  0  1 1 0 0 0 | 0 0 1 1 1 0
.o3.x .. .x ..      0  6 |  0  0  0  6  3 | 0  0  0  0  0  0  0 2  3  0  0 | *  * *  *  *  *  *  *  *  * 12  *  * * | 0 0 0  1  0  0  0  0 0 1 1 0 | 0 1 1 0 0 1
.. .x .o3.x ..      0  6 |  0  0  0  3  6 | 0  0  0  0  0  0  0 0  3  2  0 | *  * *  *  *  *  *  *  *  *  * 12  * * | 0 0 0  0  0  0  1  0 0 1 0 1 | 0 1 0 0 1 1
.. .x .. .x3.o      0  6 |  0  0  0  3  6 | 0  0  0  0  0  0  0 0  3  0  2 | *  * *  *  *  *  *  *  *  *  *  * 12 * | 0 0 0  0  0  0  0  1 0 0 1 1 | 0 0 1 0 1 1
.. .. .o3.x3.o      0  6 |  0  0  0  0 12 | 0  0  0  0  0  0  0 0  0  4  4 | *  * *  *  *  *  *  *  *  *  *  *  * 3 | 0 0 0  0  0  0  0  0 2 0 0 2 | 0 0 0 1 2 1
------------------+-------+----------------+--------------------------------+----------------------------------------+------------------------------+------------
x.3o. x.3o. ..      9  0 |  9  9  0  0  0 | 3  9  3  0  0  0  0 0  0  0  0 | 3  3 0  0  0  0  0  0  0  0  0  0  0 0 | 4 * *  *  *  *  *  * * * * * | 1 1 0 0 0 0
x. .. x.3o.3o.      8  0 |  4 12  0  0  0 | 0  6  8  0  0  0  0 0  0  0  0 | 0  4 2  0  0  0  0  0  0  0  0  0  0 0 | * 3 *  *  *  *  *  * * * * * | 1 0 0 1 0 0
xo3ox xo .. ..&#x   6  3 |  6  3 12  3  0 | 2  3  0  6  6  6  0 1  0  0  0 | 1  0 0  2  3  0  3  0  0  0  0  0  0 0 | * * 6  *  *  *  *  * * * * * | 0 2 0 0 0 0
xo3ox .. ox ..&#x   3  6 |  3  0 12  6  3 | 1  0  0  6  6  0  6 2  3  0  0 | 0  0 0  2  0  3  0  3  0  0  1  0  0 0 | * * * 12  *  *  *  * * * * * | 0 1 1 0 0 0
xo .. xo3ox ..&#x   6  3 |  3  6 12  0  3 | 0  3  2  6  0  6  6 0  0  1  0 | 0  1 0  0  3  3  0  0  2  0  0  0  0 0 | * * *  * 12  *  *  * * * * * | 0 1 0 1 0 0
xo .. .. ox3oo&#x   2  3 |  1  0  6  0  3 | 0  0  0  3  0  0  6 0  0  0  1 | 0  0 0  0  0  3  0  0  0  2  0  0  0 0 | * * *  *  * 12  *  * * * * * | 0 0 1 1 0 0
.. ox xo3ox ..&#x   3  6 |  0  3 12  3  6 | 0  0  1  0  6  6  6 0  3  2  0 | 0  0 0  0  0  0  3  3  2  0  0  1  0 0 | * * *  *  *  * 12  * * * * * | 0 1 0 0 1 0
.. ox .. ox3oo&#x   1  6 |  0  0  6  3  6 | 0  0  0  0  3  0  6 0  3  0  2 | 0  0 0  0  0  0  0  3  0  2  0  0  1 0 | * * *  *  *  *  * 12 * * * * | 0 0 1 0 1 0
.. .. xo3ox3oo&#x   4  6 |  0  6 12  0 12 | 0  0  4  0  0  6 12 0  0  4  4 | 0  0 1  0  0  0  0  0  4  4  0  0  0 1 | * * *  *  *  *  *  * 6 * * * | 0 0 0 1 1 0
.o3.x .o3.x ..      0  9 |  0  0  0  9  9 | 0  0  0  0  0  0  0 3  9  3  0 | 0  0 0  0  0  0  0  0  0  0  3  3  0 0 | * * *  *  *  *  *  * * 4 * * | 0 1 0 0 0 1
.o3.x .. .x3.o      0  9 |  0  0  0  9  9 | 0  0  0  0  0  0  0 3  9  0  3 | 0  0 0  0  0  0  0  0  0  0  3  0  3 0 | * * *  *  *  *  *  * * * 4 * | 0 0 1 0 0 1
.. .x .o3.x3.o      0 12 |  0  0  0  6 24 | 0  0  0  0  0  0  0 0 12  8  8 | 0  0 0  0  0  0  0  0  0  0  0  4  4 2 | * * *  *  *  *  *  * * * * 3 | 0 0 0 0 1 1
------------------+-------+----------------+--------------------------------+----------------------------------------+------------------------------+------------
x.3o. x.3o.3o.     12  0 | 12 18  0  0  0 | 4 18 12  0  0  0  0 0  0  0  0 | 6 12 3  0  0  0  0  0  0  0  0  0  0 0 | 4 3 0  0  0  0  0  0 0 0 0 0 | 1 * * * * *
xo3ox xo3ox ..&#x   9  9 |  9  9 36  9  9 | 3  9  3 18 18 18 18 3  9  3  0 | 3  3 0  6  9  9  9  9  6  0  3  3  0 0 | 1 0 3  3  3  0  3  0 0 1 0 0 | * 4 * * * *
xo3ox .. ox3oo&#x   3  9 |  3  0 18  9  9 | 1  0  0  9  9  0 18 3  9  0  3 | 0  0 0  3  0  9  0  9  0  6  3  0  3 0 | 0 0 0  3  0  3  0  3 0 0 1 0 | * * 4 * * *
xo .. xo3ox3oo&#x   8  6 |  4 12 24  0 12 | 0  6  8 12  0 12 24 0  0  4  4 | 0  4 2  0  6 12  0  0  8  8  0  0  0 1 | 0 1 0  0  4  4  0  0 2 0 0 0 | * * * 3 * *
.. ox xo3ox3oo&#x   4 12 |  0  6 24  6 24 | 0  0  4  0 12 12 24 0 12  8  8 | 0  0 1  0  0  0  6 12  8  8  0  4  4 2 | 0 0 0  0  0  0  4  4 2 0 0 1 | * * * * 3 *
.o3.x .o3.x3.o      0 18 |  0  0  0 18 36 | 0  0  0  0  0  0  0 6 36 12 12 | 0  0 0  0  0  0  0  0  0  0 12 12 12 3 | 0 0 0  0  0  0  0  0 0 4 4 3 | * * * * * 1

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