Acronym trial trarap
Name triangle atop inverted triangle-rectified-pentachoron duoprism
Circumradius sqrt(63/64) = 0.992157
Lace hyper city
in approx. ASCII-art
  o3x3o3o        
                 
                 
          o3x3o3o
                 
                 
  o3x3o3o        
trarap
        o3o3o3o  
                 
                 
o3o3o3o          
                 
                 
        o3o3o3o  
dual {3}
Face vector 33, 183, 431, 520, 333, 109, 17
Confer
general polytopal classes:
segmentoexa   lace simplices  

Incidence matrix according to Dynkin symbol

xo3ox oo3ox3oo3oo&#x   → height = 1/sqrt(15) = 0.258199
({3} || {3}-dual trarap)

o.3o. o.3o.3o.3o.    | 3  *  2 20  0  0 | 1 20 10  60  0  0  0  0 | 10 60 30 20  40  0  0  0  0  0 | 30 20 40 10 20 10 10  0  0  0  0 0 | 10 20 10 10  5  5 2 0 0 0 | 5 5 2 1 0
.o3.o .o3.o3.o3.o    | * 30 | 0  2  2  6 | 0  1  2  12  1 12  3  6 |  1  6 12  6  12  6  6 12  3  2 |  6  3  6  6 12  6  4  3  6  6  4 1 |  3  6  3  2  6  4 2 3 2 2 | 3 2 1 2 1
---------------------+------+------------+-------------------------+--------------------------------+------------------------------------+---------------------------+----------
x. .. .. .. .. ..    | 2  0 | 3  *  *  *  1 10  0   0  0  0  0  0 | 10 30  0  0   0  0  0  0  0  0 | 30 10 20  0  0  0  0  0  0  0  0 0 | 10 20  5  5  0  0 0 0 0 0 | 5 5 1 0 0
oo3oo oo3oo3oo3oo&#x | 1  1 | * 60  *  * | 0  1  1   6  0  0  0  0 |  1  6  6  3   6  0  0  0  0  0 |  6  3  6  3  6  3  2  0  0  0  0 0 |  3  6  3  2  3  2 1 0 0 0 | 3 2 1 1 0
.. .x .. .. .. ..    | 0  2 | *  * 30  * | 0  0  1   0  1  6  0  0 |  1  0  6  0   0  6  3  6  0  0 |  6  0  0  3  6  0  0  3  6  3  2 0 |  3  6  0  0  3  2 0 3 2 1 | 3 2 0 1 1
.. .. .. .x .. ..    | 0  2 | *  *  * 90 | 0  0  0   2  0  2  1  2 |  0  1  2  2   4  1  2  4  2  1 |  1  1  2  2  4  4  2  1  2  4  2 1 |  1  2  2  1  4  2 2 2 1 2 | 2 1 1 2 1
---------------------+------+------------+-------------------------+--------------------------------+------------------------------------+---------------------------+----------
x.3o. .. .. .. ..    | 3  0 | 3  0  0  0 | 1  *  *   *  *  *  *  *  10  0  0  0   0  0  0  0  0  0 | 30  0  0  0  0  0  0  0  0  0  0 0 | 10 20  0  0  0  0 0 0 0 0 | 5 5 0 0 0
xo .. .. .. .. ..&#x | 2  1 | 1  2  0  0 | * 30  *   *  *  *  *  * |  1  6  0  0   0  0  0  0  0  0 |  6  3  6  0  0  0  0  0  0  0  0 0 |  3  6  3  2  0  0 0 0 0 0 | 3 2 1 0 0
.. ox .. .. .. ..&#x | 1  2 | 0  2  1  0 | *  * 30   *  *  *  *  * |  1  0  6  0   0  0  0  0  0  0 |  6  0  0  3  6  0  0  0  0  0  0 0 |  3  6  0  0  3  2 0 0 0 0 | 3 2 0 1 0
.. .. .. ox .. ..&#x | 1  2 | 0  2  0  1 | *  *  * 180  *  *  *  * |  0  1  1  1   2  0  0  0  0  0 |  1  1  2  1  2  2  1  0  0  0  0 0 |  1  2  2  1  2  1 1 0 0 0 | 2 1 1 1 0
.o3.x .. .. .. ..    | 0  3 | 0  0  3  0 | *  *  *   * 10  *  *  * |  1  0  0  0   0  6  0  0  0  0 |  6  0  0  0  0  0  0  3  6  0  0 0 |  3  6  0  0  0  0 0 3 2 0 | 3 2 0 0 1
.. .x .. .x .. ..    | 0  4 | 0  0  2  2 | *  *  *   *  * 90  *  * |  0  0  1  0   0  1  1  2  0  0 |  1  0  0  1  2  0  0  1  2  2  1 0 |  1  2  0  0  2  1 0 2 1 1 | 2 1 0 1 1
.. .. .o3.x .. ..    | 0  3 | 0  0  0  3 | *  *  *   *  *  * 30  * |  0  0  0  2   0  0  2  0  2  0 |  0  1  0  2  0  4  0  1  0  4  0 1 |  1  0  2  0  4  0 2 2 0 2 | 2 0 1 2 1
.. .. .. .x3.o ..    | 0  3 | 0  0  0  3 | *  *  *   *  *  *  * 60 |  0  0  0  0   2  0  0  2  1  1 |  0  0  1  0  2  2  2  0  1  2  2 1 |  0  1  1  1  2  2 2 1 1 2 | 1 1 1 2 1
---------------------+------+------------+-------------------------+--------------------------------+------------------------------------+---------------------------+----------
xo3ox .. .. .. ..&#x  3  3 | 3  6  3  0 | 1  3  3   0  1  0  0  0 | 10  *  *  *   *  *  *  *  *  *   6  0  0  0  0  0  0  0  0  0  0 0 |  3  6  0  0  0  0 0 0 0 0 | 3 2 0 0 0
xo .. .. ox .. ..&#x  2  2 | 1  4  0  1 | 0  2  0   2  0  0  0  0 |  * 90  *  *   *  *  *  *  *  * |  1  1  2  0  0  0  0  0  0  0  0 0 |  1  2  2  1  0  0 0 0 0 0 | 2 1 1 0 0
.. ox .. ox .. ..&#x  1  4 | 0  4  2  2 | 0  0  2   2  0  1  0  0 |  *  * 90  *   *  *  *  *  *  * |  1  0  0  1  2  0  0  0  0  0  0 0 |  1  2  0  0  2  1 0 0 0 0 | 2 1 0 1 0
.. .. oo3ox .. ..&#x  1  3 | 0  3  0  3 | 0  0  0   3  0  0  1  0 |  *  *  * 60   *  *  *  *  *  * |  0  1  0  1  0  2  0  0  0  0  0 0 |  1  0  2  0  2  0 1 0 0 0 | 2 0 1 1 0
.. .. .. ox3oo ..&#x  1  3 | 0  3  0  3 | 0  0  0   3  0  0  0  1 |  *  *  *  * 120  *  *  *  *  * |  0  0  1  0  1  1  1  0  0  0  0 0 |  0  1  1  1  1  1 1 0 0 0 | 1 1 1 1 0
.o3.x .. .x .. ..     0  6 | 0  0  6  3 | 0  0  0   0  2  3  0  0 |  *  *  *  *   * 30  *  *  *  * |  1  0  0  0  0  0  0  1  2  0  0 0 |  1  2  0  0  0  0 0 2 1 0 | 2 1 0 0 1
.. .x .o3.x .. ..     0  6 | 0  0  3  6 | 0  0  0   0  0  3  2  0 |  *  *  *  *   *  * 30  *  *  * |  0  0  0  1  0  0  0  1  0  2  0 0 |  1  0  0  0  2  0 0 2 0 1 | 2 0 0 1 1
.. .x .. .x3.o ..     0  6 | 0  0  3  6 | 0  0  0   0  0  3  0  2 |  *  *  *  *   *  *  * 60  *  * |  0  0  0  0  1  0  0  0  1  1  1 0 |  0  1  0  0  1  1 0 1 1 1 | 1 1 0 1 1
.. .. .o3.x3.o ..     0  6 | 0  0  0 12 | 0  0  0   0  0  0  4  4 |  *  *  *  *   *  *  *  * 15  * |  0  0  0  0  0  2  0  0  0  2  0 1 |  0  0  1  0  2  0 2 1 0 2 | 1 0 1 2 1
.. .. .. .x3.o3.o     0  4 | 0  0  0  6 | 0  0  0   0  0  0  0  4 |  *  *  *  *   *  *  *  *  * 15 |  0  0  0  0  0  0  2  0  0  0  2 1 |  0  0  0  1  0  2 2 0 1 2 | 0 1 1 2 1
---------------------+------+------------+-------------------------+--------------------------------+------------------------------------+---------------------------+----------
xo3ox .. ox .. ..&#x  3  6 | 3 12  6  3 | 1  6  6   6  2  3  0  0 |  2  3  3  0   0  1  0  0  0  0 | 30  *  *  *  *  *  *  *  *  *  * * |  1  2  0  0  0  0 0 0 0 0 | 2 1 0 0 0
xo .. oo3ox .. ..&#x  2  3 | 1  6  0  3 | 0  3  0   6  0  0  1  0 |  0  3  0  2   0  0  0  0  0  0 |  * 30  *  *  *  *  *  *  *  *  * * |  1  0  2  0  0  0 0 0 0 0 | 2 0 1 0 0
xo .. .. ox3oo ..&#x  2  3 | 1  6  0  3 | 0  3  0   6  0  0  0  1 |  0  3  0  0   2  0  0  0  0  0 |  *  * 60  *  *  *  *  *  *  *  * * |  0  1  1  1  0  0 0 0 0 0 | 1 1 1 0 0
.. ox oo3ox .. ..&#x  1  6 | 0  6  3  6 | 0  0  3   6  0  3  2  0 |  0  0  3  2   0  0  1  0  0  0 |  *  *  * 30  *  *  *  *  *  *  * * |  1  0  0  0  2  0 0 0 0 0 | 2 0 0 1 0
.. ox .. ox3oo ..&#x  1  6 | 0  6  3  6 | 0  0  3   6  0  3  0  2 |  0  0  3  0   2  0  0  1  0  0 |  *  *  *  * 60  *  *  *  *  *  * * |  0  1  0  0  1  1 0 0 0 0 | 1 1 0 1 0
.. .. oo3ox3oo ..&#x  1  6 | 0  6  0 12 | 0  0  0  12  0  0  4  4 |  0  0  0  4   4  0  0  0  1  0 |  *  *  *  *  * 30  *  *  *  *  * * |  0  0  1  0  1  0 1 0 0 0 | 1 0 1 1 0
.. .. .. ox3oo3oo&#x  1  4 | 0  4  0  6 | 0  0  0   6  0  0  0  4 |  0  0  0  0   4  0  0  0  0  1 |  *  *  *  *  *  * 30  *  *  *  * * |  0  0  0  1  0  1 1 0 0 0 | 0 1 1 1 0
.o3.x .o3.x .. ..     0  9 | 0  0  9  9 | 0  0  0   0  3  9  3  0 |  0  0  0  0   0  3  3  0  0  0 |  *  *  *  *  *  *  * 10  *  *  * * |  1  0  0  0  0  0 0 2 0 0 | 2 0 0 0 1
.o3.x .. .x3.o ..     0  9 | 0  0  9  9 | 0  0  0   0  3  9  0  3 |  0  0  0  0   0  3  0  3  0  0 |  *  *  *  *  *  *  *  * 20  *  * * |  0  1  0  0  0  0 0 1 1 0 | 1 1 0 0 1
.. .x .o3.x3.o ..     0 12 | 0  0  6 24 | 0  0  0   0  0 12  8  8 |  0  0  0  0   0  0  4  4  2  0 |  *  *  *  *  *  *  *  *  * 15  * * |  0  0  0  0  1  0 0 1 0 1 | 1 0 0 1 1
.. .x .. .x3.o3.o     0  8 | 0  0  4 12 | 0  0  0   0  0  6  0  8 |  0  0  0  0   0  0  0  4  0  2 |  *  *  *  *  *  *  *  *  *  * 15 * |  0  0  0  0  0  1 0 0 1 1 | 0 1 0 1 1
.. .. .o3.x3.o3.o     0 10 | 0  0  0 30 | 0  0  0   0  0  0 10 20 |  0  0  0  0   0  0  0  0  5  5 |  *  *  *  *  *  *  *  *  *  *  * 3 |  0  0  0  0  0  0 2 0 0 2 | 0 0 1 2 1
---------------------+------+------------+-------------------------+--------------------------------+------------------------------------+---------------------------+----------
xo3ox oo3ox .. ..&#x  3  9 | 3 18  9  9 | 1  9  9  18  3  9  3  0 |  3  9  9  6   0  3  3  0  0  0 |  3  3  0  3  0  0  0  1  0  0  0 0 | 10  *  *  *  *  * * * * * | 2 0 0 0 0
xo3ox .. ox3oo ..&#x  3  9 | 3 18  9  9 | 1  9  9  18  3  9  0  3 |  3  9  9  0   6  3  0  3  0  0 |  3  0  3  0  3  0  0  0  1  0  0 0 |  * 20  *  *  *  * * * * * | 1 1 0 0 0
xo .. oo3ox3oo ..&#x  2  6 | 1 12  0 12 | 0  6  0  24  0  0  4  4 |  0 12  0  8   8  0  0  0  1  0 |  0  4  4  0  0  2  0  0  0  0  0 0 |  *  * 15  *  *  * * * * * | 1 0 1 0 0
xo .. .. ox3oo3oo&#x  2  4 | 1  8  0  6 | 0  4  0  12  0  0  0  4 |  0  6  0  0   8  0  0  0  0  1 |  0  0  4  0  0  0  2  0  0  0  0 0 |  *  *  * 15  *  * * * * * | 0 1 1 0 0
.. ox oo3ox3oo ..&#x  1 12 | 0 12  6 24 | 0  0  6  24  0 12  8  8 |  0  0 12  8   8  0  4  4  2  0 |  0  0  0  4  4  2  0  0  0  1  0 0 |  *  *  *  * 15  * * * * * | 1 0 0 1 0
.. ox .. ox3oo3oo&#x  1  8 | 0  8  4 12 | 0  0  4  12  0  6  0  8 |  0  0  6  0   8  0  0  4  0  2 |  0  0  0  0  4  0  2  0  0  0  1 0 |  *  *  *  *  * 15 * * * * | 0 1 0 1 0
.. .. oo3ox3oo3oo&#x  1 10 | 0 10  0 30 | 0  0  0  30  0  0 10 20 |  0  0  0 10  20  0  0  0  5  5 |  0  0  0  0  0  5  5  0  0  0  0 1 |  *  *  *  *  *  * 6 * * * | 0 0 1 1 0
.o3.x .o3.x3.o ..     0 18 | 0  0 18 36 | 0  0  0   0  6 36 12 12 |  0  0  0  0   0 12 12 12  3  0 |  0  0  0  0  0  0  0  4  4  3  0 0 |  *  *  *  *  *  * * 5 * * | 1 0 0 0 1
.o3.x .. .x3.o3.o     0 12 | 0  0 12 18 | 0  0  0   0  4 18  0 12 |  0  0  0  0   0  6  0 12  0  3 |  0  0  0  0  0  0  0  0  4  0  3 0 |  *  *  *  *  *  * * * 5 * | 0 1 0 0 1
.. .x .o3.x3.o3.o     0 20 | 0  0 10 60 | 0  0  0   0  0 30 20 40 |  0  0  0  0   0  0 10 20 10 10 |  0  0  0  0  0  0  0  0  0  5  5 2 |  *  *  *  *  *  * * * * 3 | 0 0 0 1 1
---------------------+------+------------+-------------------------+--------------------------------+------------------------------------+---------------------------+----------
xo3ox oo3ox3oo ..&#x  3 18 | 3 36 18 36 | 1 18 18  72  6 36 12 12 |  6 36 36 24  24 12 12 12  3  0 | 12 12 12 12 12  6  0  4  4  3  0 0 |  4  4  3  0  3  0 0 1 0 0 | 5 * * * *
xo3ox .. ox3oo3oo&#x  3 12 | 3 24 12 18 | 1 12 12  36  4 18  0 12 |  4 18 18  0  24  6  0 12  0  3 |  6  0 12  0 12  0  6  0  4  0  3 0 |  0  4  0  3  0  3 0 0 1 0 | * 5 * * *
xo .. oo3ox3oo3oo&#x  2 10 | 1 20  0 30 | 0 10  0  60  0  0 10 20 |  0 30  0 20  40  0  0  0  5  5 |  0 10 20  0  0 10 10  0  0  0  0 1 |  0  0  5  5  0  0 2 0 0 0 | * * 3 * *
.. ox oo3ox3oo3oo&#x  1 20 | 0 20 10 60 | 0  0 10  60  0 30 20 40 |  0  0 30 20  40  0 10 20 10 10 |  0  0  0 10 20 10 10  0  0  5  5 2 |  0  0  0  0  5  5 2 0 0 1 | * * * 3 *
.o3.x .o3.x3.o3.o     0 30 | 0  0 30 90 | 0  0  0   0 10 90 30 60 |  0  0  0  0   0 30 30 60 15 15 |  0  0  0  0  0  0  0 10 20 15 15 3 |  0  0  0  0  0  0 0 5 5 3 | * * * * 1

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