Acronym rapatrapen
Name rectified pentachoron atop triangle-pentachoron duoprism,
rap-first cap of roc
Circumradius sqrt(3)/2 = 0.866025
Lace hyper city
in approx. ASCII-art
                 
                 
                 
     o3x3o3o     
                 
                 
                 
rap
  x3o3o3o        
                 
                 
          x3o3o3o
                 
                 
  x3o3o3o        
trapen
Face vector 25, 135, 275, 295, 189, 71, 14
Confer
uniform relative:
roc  
general polytopal classes:
segmentoexa   lace simplices  

Incidence matrix according to Dynkin symbol

ox3oo ox3xo3oo3oo&#x   → height = 2/sqrt(15) = 0.516398
(rap || trapen)

o.3o. o.3o.3o.3o.    | 10  *   6  6  0  0 |  3  6  6  3 18 0  0  0 | 3 2  2  3 18  9 18  0  0  0 | 1  1  6  9 18  9  6  0  0 0 |  3  6  9  6 3 0 0 | 3 2 3 0
.o3.o .o3.o3.o3.o    |  * 15 |  0  4  2  4 |  0  0  8  4  6 1  8  6 | 0 0  4  8 12  6  4  4 12  4 | 0  4  6 12  8  4  1  6  8 1 |  6  4  8  2 1 4 2 | 4 1 2 1
---------------------+-------+-------------+------------------------+-----------------------------+-----------------------------+-------------------+--------
.. .. .. x. .. ..    |  2  0 | 30  *  *  * |  1  2  0  0  3 0  0  0 | 2 1  0  0  3  3  6  0  0  0 | 1  0  1  3  6  6  3  0  0 0 |  1  2  6  3 3 0 0 | 2 1 3 0
oo3oo oo3oo3oo3oo&#x |  1  1 |  * 60  *  * |  0  0  2  1  3 0  0  0 | 0 0  1  2  6  3  3  0  0  0 | 0  1  3  6  6  3  1  0  0 0 |  3  3  6  2 1 0 0 | 3 1 2 0
.x .. .. .. .. ..    |  0  2 |  *  * 15  * |  0  0  4  0  0 1  4  0 | 0 0  4  4  6  0  0  4  6  0 | 0  4  6  6  4  0  0  6  4 0 |  6  4  4  1 0 4 1 | 4 1 1 1
.. .. .x .. .. ..    |  0  2 |  *  *  * 30 |  0  0  0  1  0 0  2  3 | 0 0  0  2  0  3  0  1  6  3 | 0  1  0  6  0  3  0  3  2 1 |  3  0  6  0 1 3 2 | 3 0 2 1
---------------------+-------+-------------+------------------------+-----------------------------+-----------------------------+-------------------+--------
.. .. o.3x. .. ..    |  3  0 |  3  0  0  0 | 10  *  *  *  * *  *  *  2 0  0  0  0  3  0  0  0  0 | 1  0  0  3  0  6  0  0  0 0 |  1  0  6  0 3 0 0 | 2 0 3 0
.. .. .. x.3o. ..    |  3  0 |  3  0  0  0 |  * 20  *  *  * *  *  * | 1 1  0  0  0  0  3  0  0  0 | 1  0  0  0  3  3  3  0  0 0 |  0  1  3  3 3 0 0 | 1 1 3 0
ox .. .. .. .. ..&#x |  1  2 |  0  2  1  0 |  *  * 60  *  * *  *  * | 0 0  1  1  3  0  0  0  0  0 | 0  1  3  3  3  0  0  0  0 0 |  3  3  3  1 0 0 0 | 3 1 1 0
.. .. ox .. .. ..&#x |  1  2 |  0  2  0  1 |  *  *  * 30  * *  *  *  0 0  0  2  0  3  0  0  0  0 | 0  1  0  6  0  3  0  0  0 0 |  3  0  6  0 1 0 0 | 3 0 2 0
.. .. .. xo .. ..&#x |  2  1 |  1  2  0  0 |  *  *  *  * 90 *  *  * | 0 0  0  0  2  1  2  0  0  0 | 0  0  1  2  4  2  1  0  0 0 |  1  2  4  2 1 0 0 | 2 1 2 0
.x3.o .. .. .. ..    |  0  3 |  0  0  3  0 |  *  *  *  *  * 5  *  * | 0 0  4  0  0  0  0  4  0  0 | 0  4  6  0  0  0  0  6  0 0 |  6  4  0  0 0 4 0 | 4 1 0 1
.x .. .x .. .. ..    |  0  4 |  0  0  2  2 |  *  *  *  *  * * 30  * | 0 0  0  1  0  0  0  1  3  0 | 0  1  0  3  0  0  0  3  3 0 |  3  0  3  0 0 3 1 | 3 0 1 1
.. .. .x3.o .. ..    |  0  3 |  0  0  0  3 |  *  *  *  *  * *  * 30 | 0 0  0  0  0  1  0  0  2  2 | 0  0  0  2  0  2  0  1  4 1 |  1  0  4  0 1 2 2 | 2 0 2 1
---------------------+-------+-------------+------------------------+-----------------------------+-----------------------------+-------------------+--------
.. .. o.3x.3o. ..      6  0 | 12  0  0  0 |  4  4  0  0  0 0  0  0 | 5 *  *  *  *  *  *  *  *  *  1  0  0  0  0  3  0  0  0 0 |  0  0  3  0 3 0 0 | 1 0 3 0
.. .. .. x.3o.3o.      4  0 |  6  0  0  0 |  0  4  0  0  0 0  0  0 | * 5  *  *  *  *  *  *  *  * | 1  0  0  0  0  0  3  0  0 0 |  0  0  0  3 3 0 0 | 0 1 3 0
ox3oo .. .. .. ..&#x   1  3 |  0  3  3  0 |  0  0  3  0  0 1  0  0 | * * 20  *  *  *  *  *  *  * | 0  1  3  0  0  0  0  0  0 0 |  3  3  0  0 0 0 0 | 3 1 0 0
ox .. ox .. .. ..&#x   1  4 |  0  4  2  2 |  0  0  2  2  0 0  1  0 | * *  * 30  *  *  *  *  *  *  0  1  0  3  0  0  0  0  0 0 |  3  0  3  0 0 0 0 | 3 0 1 0
ox .. .. xo .. ..&#x   2  2 |  1  4  1  0 |  0  0  2  0  2 0  0  0 | * *  *  * 90  *  *  *  *  * | 0  0  1  1  2  0  0  0  0 0 |  1  2  2  1 0 0 0 | 2 1 1 0
.. .. ox3xo .. ..&#x   3  3 |  3  6  0  3 |  1  0  0  3  3 0  0  1 | * *  *  *  * 30  *  *  *  *  0  0  0  2  0  2  0  0  0 0 |  1  0  4  0 1 0 0 | 2 0 2 0
.. .. .. xo3oo ..&#x   3  1 |  3  3  0  0 |  0  1  0  0  3 0  0  0 | * *  *  *  *  * 60  *  *  * | 0  0  0  0  2  1  1  0  0 0 |  0  1  2  2 1 0 0 | 1 1 2 0
.x3.o .x .. .. ..      0  6 |  0  0  6  3 |  0  0  0  0  0 2  3  0 | * *  *  *  *  *  * 10  *  * | 0  1  0  0  0  0  0  3  0 0 |  3  0  0  0 0 3 0 | 3 0 0 1
.x .. .x3.o .. ..      0  6 |  0  0  3  6 |  0  0  0  0  0 0  3  2 | * *  *  *  *  *  *  * 30  * | 0  0  0  1  0  0  0  1  2 0 |  1  0  2  0 0 2 1 | 2 0 1 1
.. .. .x3.o3.o ..      0  4 |  0  0  0  6 |  0  0  0  0  0 0  0  4 | * *  *  *  *  *  *  *  * 15 | 0  0  0  0  0  1  0  0  2 1 |  0  0  2  0 1 1 2 | 1 0 2 1
---------------------+-------+-------------+------------------------+-----------------------------+-----------------------------+-------------------+--------
.. .. o.3x.3o.3o.     10  0 | 30  0  0  0 | 10 20  0  0  0 0  0  0 | 5 5  0  0  0  0  0  0  0  0 | 1  *  *  *  *  *  *  *  * * |  0  0  0  0 3 0 0 | 0 0 3 0
ox3oo ox .. .. ..&#x   1  6 |  0  6  6  3 |  0  0  6  3  0 2  3  0 | 0 0  2  3  0  0  0  1  0  0 | * 10  *  *  *  *  *  *  * * |  3  0  0  0 0 0 0 | 3 0 0 0
ox3oo .. xo .. ..&#x   2  3 |  1  6  3  0 |  0  0  6  0  3 1  0  0 | 0 0  2  0  3  0  0  0  0  0 | *  * 30  *  *  *  *  *  * * |  1  2  0  0 0 0 0 | 2 1 0 0
ox .. ox3xo .. ..&#x   3  6 |  3 12  3  6 |  1  0  6  6  6 0  3  2 | 0 0  0  3  3  2  0  0  1  0 | *  *  * 30  *  *  *  *  * * |  1  0  2  0 0 0 0 | 2 0 1 0
ox .. .. xo3oo ..&#x   3  2 |  3  6  1  0 |  0  1  3  0  6 0  0  0 | 0 0  0  0  3  0  2  0  0  0 | *  *  *  * 60  *  *  *  * * |  0  1  1  1 0 0 0 | 1 1 1 0
.. .. ox3xo3oo ..&#x   6  4 | 12 12  0  6 |  4  4  0  6 12 0  0  4 | 1 0  0  0  0  4  4  0  0  1 | *  *  *  *  * 15  *  *  * * |  0  0  2  0 1 0 0 | 1 0 2 0
.. .. .. xo3oo3oo&#x   4  1 |  6  4  0  0 |  0  4  0  0  6 0  0  0 | 0 1  0  0  0  0  4  0  0  0 | *  *  *  *  *  * 15  *  * * |  0  0  0  2 1 0 0 | 0 1 2 0
.x3.o .x3.o .. ..      0  9 |  0  0  9  9 |  0  0  0  0  0 3  9  3 | 0 0  0  0  0  0  0  3  3  0 | *  *  *  *  *  *  * 10  * * |  1  0  0  0 0 2 0 | 2 0 0 1
.x .. .x3.o3.o ..      0  8 |  0  0  4 12 |  0  0  0  0  0 0  6  8 | 0 0  0  0  0  0  0  0  4  2 | *  *  *  *  *  *  *  * 15 * |  0  0  1  0 0 1 1 | 1 0 1 1
.. .. .x3.o3.o3.o      0  5 |  0  0  0 10 |  0  0  0  0  0 0  0 10 | 0 0  0  0  0  0  0  0  0  5 | *  *  *  *  *  *  *  *  * 3 |  0  0  0  0 1 0 2 | 0 0 2 1
---------------------+-------+-------------+------------------------+-----------------------------+-----------------------------+-------------------+--------
ox3oo ox3xo .. ..&#x   3  9 |  3 18  9  9 |  1  0 18  9  9 3  9  3 | 0 0  6  9  9  3  0  3  3  0 | 0  3  3  3  0  0  0  1  0 0 | 10  *  *  * * * * | 2 0 0 0
ox3oo .. xo3oo ..&#x   3  3 |  3  9  3  0 |  0  1  9  0  9 1  0  0 | 0 0  3  0  9  0  3  0  0  0 | 0  0  3  0  3  0  0  0  0 0 |  * 20  *  * * * * | 1 1 0 0
ox .. ox3xo3oo ..&#x   6  8 | 12 24  4 12 |  4  4 12 12 24 0  6  8 | 1 0  0  6 12  8  8  0  4  2 | 0  0  0  4  4  2  0  0  1 0 |  *  * 15  * * * * | 1 0 1 0
ox .. .. xo3oo3oo&#x   4  2 |  6  8  1  0 |  0  4  4  0 12 0  0  0 | 0 1  0  0  6  0  8  0  0  0 | 0  0  0  0  4  0  2  0  0 0 |  *  *  * 15 * * * | 0 1 1 0
.. .. ox3xo3oo3oo&#x  10  5 | 30 20  0 10 | 10 20  0 10 30 0  0 10 | 5 5  0  0  0 10 20  0  0  5 | 1  0  0  0  0  5  5  0  0 1 |  *  *  *  * 3 * * | 0 0 2 0
.x3.o .x3.o3.o ..      0 12 |  0  0 12 18 |  0  0  0  0  0 4 18 12 | 0 0  0  0  0  0  0  6 12  3 | 0  0  0  0  0  0  0  4  3 0 |  *  *  *  * * 5 * | 1 0 0 1
.x .. .x3.o3.o3.o      0 10 |  0  0  5 20 |  0  0  0  0  0 0 10 20 | 0 0  0  0  0  0  0  0 10 10 | 0  0  0  0  0  0  0  0  5 2 |  *  *  *  * * * 3 | 0 0 1 1
---------------------+-------+-------------+------------------------+-----------------------------+-----------------------------+-------------------+--------
ox3oo ox3xo3oo ..&#x   6 12 | 12 36 12 18 |  4  4 36 18 36 4 18 12 | 1 0 12 18 36 12 12  6 12  3 | 0  6 12 12 12  3  0  4  3 0 |  4  4  3  0 0 1 0 | 5 * * *
ox3oo .. xo3oo3oo&#x   4  3 |  6 12  3  0 |  0  4 12  0 18 1  0  0 | 0 1  4  0 18  0 12  0  0  0 | 0  0  6  0 12  0  3  0  0 0 |  0  4  0  3 0 0 0 | * 5 * *
ox .. ox3xo3oo3oo&#x  10 10 | 30 40  5 20 | 10 20 20 20 60 0 10 20 | 5 5  0 10 30 20 40  0 10 10 | 1  0  0 10 20 10 10  0  5 2 |  0  0  5  5 2 0 1 | * * 3 *
.x3.o .x3.o3.o3.o      0 15 |  0  0 15 30 |  0  0  0  0  0 5 30 30 | 0 0  0  0  0  0  0 10 30 15 | 0  0  0  0  0  0  0 10 15 3 |  0  0  0  0 0 5 3 | * * * 1

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