Acronym rappippy
Name rectified-pentachoron-prismatic pyramid,
vertex pyramid of rectified icosiheptaheptacontidipeton
Circumradius sqrt(5/3) = 1.290994
Lace city
in approx. ASCII-art
   o            R = rap
R     R         o = point
Face vector 21, 90, 160, 140, 62, 13
Confer
uniform relative:
rojak  
general polytopal classes:
segmentopeta   lace simplices  

Incidence matrix according to Dynkin symbol

ox oo3ox3oo3oo&#x   → height = sqrt(3/20) = 0.387298
(pt || rappip)

o. o.3o.3o.3o.    | 1  *  20  0  0 | 10 60  0  0  0 | 30 20 40  0  0  0  0 | 10 20 10 10 0 0 0 | 5 5 2 0
.o .o3.o3.o3.o    | * 20 |  1  1  6 |  1  6  6  3  6 |  6  3  6  3  6  3  2 |  3  6  3  2 3 2 1 | 3 2 1 1
------------------+------+----------+----------------+----------------------+-------------------+--------
oo oo3oo3oo3oo&#x | 1  1 | 20  *  * |  1  6  0  0  0 |  6  3  6  0  0  0  0 |  3  6  3  2 0 0 0 | 3 2 1 0
.x .. .. .. ..    | 0  2 |  * 10  * |  1  0  6  0  0 |  6  0  0  3  6  0  0 |  3  6  0  0 3 2 0 | 3 2 0 1
.. .. .x .. ..    | 0  2 |  *  * 60 |  0  1  1  1  2 |  1  1  2  1  2  2  1 |  1  2  2  1 2 1 1 | 2 1 1 1
------------------+------+----------+----------------+----------------------+-------------------+--------
ox .. .. .. ..&#x | 1  2 |  2  1  0 | 10  *  *  *  *   6  0  0  0  0  0  0 |  3  6  0  0 0 0 0 | 3 2 0 0
.. .. ox .. ..&#x | 1  2 |  2  0  1 |  * 60  *  *  * |  1  1  2  0  0  0  0 |  1  2  2  1 0 0 0 | 2 1 1 0
.x .. .x .. ..    | 0  4 |  0  2  2 |  *  * 30  *  * |  1  0  0  1  2  0  0 |  1  2  0  0 2 1 0 | 2 1 0 1
.. .o3.x .. ..    | 0  3 |  0  0  3 |  *  *  * 20  * |  0  1  0  1  0  2  0 |  1  0  2  0 2 0 1 | 2 0 1 1
.. .. .x3.o ..    | 0  3 |  0  0  3 |  *  *  *  * 40 |  0  0  1  0  1  1  1 |  0  1  1  1 1 1 1 | 1 1 1 1
------------------+------+----------+----------------+----------------------+-------------------+--------
ox .. ox .. ..&#x  1  4 |  4  2  2 |  2  2  1  0  0 | 30  *  *  *  *  *  * |  1  2  0  0 0 0 0 | 2 1 0 0
.. oo3ox .. ..&#x  1  3 |  3  0  3 |  0  3  0  1  0 |  * 20  *  *  *  *  * |  1  0  2  0 0 0 0 | 2 0 1 0
.. .. ox3oo ..&#x  1  3 |  3  0  3 |  0  3  0  0  1 |  *  * 40  *  *  *  * |  0  1  1  1 0 0 0 | 1 1 1 0
.x .o3.x .. ..     0  6 |  0  3  6 |  0  0  3  2  0 |  *  *  * 10  *  *  * |  1  0  0  0 2 0 0 | 2 0 0 1
.x .. .x3.o ..     0  6 |  0  3  6 |  0  0  3  0  2 |  *  *  *  * 20  *  * |  0  1  0  0 1 1 0 | 1 1 0 1
.. .o3.x3.o ..     0  6 |  0  0 12 |  0  0  0  4  4 |  *  *  *  *  * 10  * |  0  0  1  0 1 0 1 | 1 0 1 1
.. .. .x3.o3.o     0  4 |  0  0  6 |  0  0  0  0  4 |  *  *  *  *  *  * 10 |  0  0  0  1 0 1 1 | 0 1 1 1
------------------+------+----------+----------------+----------------------+-------------------+--------
ox oo3ox .. ..&#x  1  6 |  6  3  6 |  3  6  3  2  0 |  3  2  0  1  0  0  0 | 10  *  *  * * * * | 2 0 0 0
ox .. ox3oo ..&#x  1  6 |  6  3  6 |  3  6  3  0  2 |  3  0  2  0  1  0  0 |  * 20  *  * * * * | 1 1 0 0
.. oo3ox3oo ..&#x  1  6 |  6  0 12 |  0 12  0  4  4 |  0  4  4  0  0  1  0 |  *  * 10  * * * * | 1 0 1 0
.. .. ox3oo3oo&#x  1  4 |  4  0  6 |  0  6  0  0  4 |  0  0  4  0  0  0  1 |  *  *  * 10 * * * | 0 1 1 0
.x .o3.x3.o ..     0 12 |  0  6 24 |  0  0 12  8  8 |  0  0  0  4  4  2  0 |  *  *  *  * 5 * * | 1 0 0 1
.x .. .x3.o3.o     0  8 |  0  4 12 |  0  0  6  0  8 |  0  0  0  0  4  0  2 |  *  *  *  * * 5 * | 0 1 0 1
.. .o3.x3.o3.o     0 10 |  0  0 30 |  0  0  0 10 20 |  0  0  0  0  0  5  5 |  *  *  *  * * * 2 | 0 0 1 1
------------------+------+----------+----------------+----------------------+-------------------+--------
ox oo3ox3oo ..&#x  1 12 | 12  6 24 |  6 24 12  8  8 | 12  8  8  4  4  2  0 |  4  4  2  0 1 0 0 | 5 * * *
ox .. ox3oo3oo&#x  1  8 |  8  4 12 |  4 12  6  0  8 |  6  0  8  0  4  0  2 |  0  4  0  2 0 1 0 | * 5 * *
.. oo3ox3oo3oo&#x  1 10 | 10  0 30 |  0 30  0 10 20 |  0 10 20  0  0  5  5 |  0  0  5  5 0 0 1 | * * 2 *
.x .o3.x3.o3.o     0 20 |  0 10 60 |  0  0 30 20 40 |  0  0  0 10 20 10 10 |  0  0  0  0 5 5 2 | * * * 1

ooo3ooo3xox3ooo&#x

o..3o..3o..3o..    | 10 *  * |  6  1  1  0  0 |  6  3  6  1  6  0  0  0 | 2 3  6  3  6  6  3  0  0 0 0 | 1 2 3  6  3 2 3 0 0 0 | 1 2 3 1 0
.o.3.o.3.o.3.o.    |  * 1  *   0 10  0 10  0 |  0  0 30 10  0 30  0  0 | 0 0 20 10 30  0  0 20 10 0 0 | 0 5 5 20 10 0 0 5 5 0 | 1 5 5 0 1
..o3..o3..o3..o    |  * * 10 |  0  0  1  1  6 |  0  0  0  1  6  6  6  3 | 0 0  0  0  6  6  3  6  3 2 3 | 0 0 0  6  3 2 3 2 3 1 | 0 2 3 1 1
-------------------+---------+----------------+-------------------------+------------------------------+-----------------------+----------
... ... x.. ...    |  2 0  0 | 30  *  *  *  * |  2  1  1  0  1  0  0  0 | 1 2  2  1  1  2  1  0  0 0 0 | 1 1 2  2  1 1 2 0 0 0 | 1 1 2 1 0
oo.3oo.3oo.3oo.&#x |  1 1  0 |  * 10  *  *  * |  0  0  6  1  0  0  0  0 | 0 0  6  3  6  0  0  0  0 0 0 | 0 2 3  6  3 0 0 0 0 0 | 1 2 3 0 0
o.o3o.o3o.o3o.o&#x |  1 0  1 |  *  * 10  *  * |  0  0  0  1  6  0  0  0 | 0 0  0  0  6  6  3  0  0 0 0 | 0 0 0  6  3 2 3 0 0 0 | 0 2 3 1 0
.oo3.oo3.oo3.oo&#x |  0 1  1 |  *  *  * 10  * |  0  0  0  1  0  6  0  0 | 0 0  0  0  6  0  0  6  3 0 0 | 0 0 0  6  3 0 0 2 3 0 | 0 2 3 0 1
... ... ..x ...    |  0 0  2 |  *  *  *  * 30 |  0  0  0  0  1  1  2  1 | 0 0  0  0  1  2  1  2  1 1 2 | 0 0 0  2  1 1 2 1 2 1 | 0 1 2 1 1
-------------------+---------+----------------+-------------------------+------------------------------+-----------------------+----------
... o..3x.. ...    |  3 0  0 |  3  0  0  0  0 | 20  *  *  *  *  *  *  * | 1 1  1  0  0  1  0  0  0 0 0 | 1 1 1  1  0 1 1 0 0 0 | 1 1 1 1 0
... ... x..3o..    |  3 0  0 |  3  0  0  0  0 |  * 10  *  *  *  *  *  * | 0 2  0  1  0  0  1  0  0 0 0 | 1 0 2  0  1 0 2 0 0 0 | 1 0 2 1 0
... ... xo. ...&#x |  2 1  0 |  1  2  0  0  0 |  *  * 30  *  *  *  *  * | 0 0  2  1  1  0  0  0  0 0 0 | 0 1 2  2  1 0 0 0 0 0 | 1 1 2 0 0
ooo3ooo3ooo3ooo&#x |  1 1  1 |  0  1  1  1  0 |  *  *  * 10  *  *  *  *  0 0  0  0  6  0  0  0  0 0 0 | 0 0 0  6  3 0 0 0 0 0 | 0 2 3 0 0
... ... x.x ...&#x |  2 0  2 |  1  0  2  0  1 |  *  *  *  * 30  *  *  * | 0 0  0  0  1  2  1  0  0 0 0 | 0 0 0  2  1 1 2 0 0 0 | 0 1 2 1 0
... ... .ox ...&#x |  0 1  2 |  0  0  0  2  1 |  *  *  *  *  * 30  *  * | 0 0  0  0  1  0  0  2  1 0 0 | 0 0 0  2  1 0 0 1 2 0 | 0 1 2 0 1
... ..o3..x ...    |  0 0  3 |  0  0  0  0  3 |  *  *  *  *  *  * 20  * | 0 0  0  0  0  1  0  1  0 1 1 | 0 0 0  1  0 1 1 1 1 1 | 0 1 1 1 1
... ... ..x3..o    |  0 0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 10 | 0 0  0  0  0  0  1  0  1 0 2 | 0 0 0  0  1 0 2 0 2 1 | 0 0 2 1 1
-------------------+---------+----------------+-------------------------+------------------------------+-----------------------+----------
o..3o..3x.. ...      4 0  0 |  6  0  0  0  0 |  4  0  0  0  0  0  0  0 | 5 *  *  *  *  *  *  *  * * * | 1 1 0  0  0 1 0 0 0 0 | 1 1 0 1 0
... o..3x..3o..      6 0  0 | 12  0  0  0  0 |  4  4  0  0  0  0  0  0 | * 5  *  *  *  *  *  *  * * * | 1 0 1  0  0 0 1 0 0 0 | 1 0 1 1 0
... oo.3xo. ...&#x   3 1  0 |  3  3  0  0  0 |  1  0  3  0  0  0  0  0 | * * 20  *  *  *  *  *  * * * | 0 1 1  1  0 0 0 0 0 0 | 1 1 1 0 0
... ... xo.3oo.&#x   3 1  0 |  3  3  0  0  0 |  0  1  3  0  0  0  0  0 | * *  * 10  *  *  *  *  * * * | 0 0 2  0  1 0 0 0 0 0 | 1 0 2 0 0
... ... xox ...&#x   2 1  2 |  1  2  2  2  1 |  0  0  1  2  1  1  0  0 | * *  *  * 30  *  *  *  * * * | 0 0 0  2  1 0 0 0 0 0 | 0 1 2 0 0
... o.o3x.x ...&#x   3 0  3 |  3  0  3  0  3 |  1  0  0  0  3  0  1  0 | * *  *  *  * 20  *  *  * * * | 0 0 0  1  0 1 1 0 0 0 | 0 1 1 1 0
... ... x.x3o.o&#x   3 0  3 |  3  0  3  0  3 |  0  1  0  0  3  0  0  1 | * *  *  *  *  * 10  *  * * * | 0 0 0  0  1 0 2 0 0 0 | 0 0 2 1 0
... .oo3.ox ...&#x   0 1  3 |  0  0  0  3  3 |  0  0  0  0  0  3  1  0 | * *  *  *  *  *  * 20  * * * | 0 0 0  1  0 0 0 1 1 0 | 0 1 1 0 1
... ... .ox3.oo&#x   0 1  3 |  0  0  0  3  3 |  0  0  0  0  0  3  0  1 | * *  *  *  *  *  *  * 10 * * | 0 0 0  0  1 0 0 0 2 0 | 0 0 2 0 1
..o3..o3..x ...      0 0  4 |  0  0  0  0  6 |  0  0  0  0  0  0  4  0 | * *  *  *  *  *  *  *  * 5 * | 0 0 0  0  0 1 0 1 0 1 | 0 1 0 1 1
... ..o3..x3..o      0 0  6 |  0  0  0  0 12 |  0  0  0  0  0  0  4  4 | * *  *  *  *  *  *  *  * * 5 | 0 0 0  0  0 0 1 0 1 1 | 0 0 1 1 1
-------------------+---------+----------------+-------------------------+------------------------------+-----------------------+----------
o..3o..3x..3o..     10 0  0 | 30  0  0  0  0 | 20 10  0  0  0  0  0  0 | 5 5  0  0  0  0  0  0  0 0 0 | 1 * *  *  * * * * * * | 1 0 0 1 0
oo.3oo.3xo. ...&#x   4 1  0 |  6  4  0  0  0 |  4  0  6  0  0  0  0  0 | 1 0  4  0  0  0  0  0  0 0 0 | * 5 *  *  * * * * * * | 1 1 0 0 0
... oo.3xo.3oo.&#x   6 1  0 | 12  6  0  0  0 |  4  4 12  0  0  0  0  0 | 0 1  4  4  0  0  0  0  0 0 0 | * * 5  *  * * * * * * | 1 0 1 0 0
... ooo3xox ...&#x   3 1  3 |  3  3  3  3  3 |  1  0  3  3  3  3  1  0 | 0 0  1  0  3  1  0  1  0 0 0 | * * * 20  * * * * * * | 0 1 1 0 0
... ... xox3ooo&#x   3 1  3 |  3  3  3  3  3 |  0  1  3  3  3  3  0  1 | 0 0  0  1  3  0  1  0  1 0 0 | * * *  * 10 * * * * * | 0 0 2 0 0
o.o3o.o3x.x ...&#x   4 0  4 |  6  0  4  0  6 |  4  0  0  0  6  0  4  0 | 1 0  0  0  0  4  0  0  0 1 0 | * * *  *  * 5 * * * * | 0 1 0 1 0
... o.o3x.x3o.o&#x   6 0  6 | 12  0  6  0 12 |  4  4  0  0 12  0  4  4 | 0 1  0  0  0  4  4  0  0 0 1 | * * *  *  * * 5 * * * | 0 0 1 1 0
.oo3.oo3.ox ...&#x   0 1  4 |  0  0  0  4  6 |  0  0  0  0  0  6  4  0 | 0 0  0  0  0  0  0  4  0 1 0 | * * *  *  * * * 5 * * | 0 1 0 0 1
... .oo3.ox3.oo&#x   0 1  6 |  0  0  0  6 12 |  0  0  0  0  0 12  4  4 | 0 0  0  0  0  0  0  4  4 0 1 | * * *  *  * * * * 5 * | 0 0 1 0 1
..o3..o3..x3..o      0 0 10 |  0  0  0  0 30 |  0  0  0  0  0  0 20 10 | 0 0  0  0  0  0  0  0  0 5 5 | * * *  *  * * * * * 1 | 0 0 0 1 1
-------------------+---------+----------------+-------------------------+------------------------------+-----------------------+----------
oo.3oo.3xo.3oo.&#x  10 1  0 | 30 10  0  0  0 | 20 10 30  0  0  0  0  0 | 5 5 20 10  0  0  0  0  0 0 0 | 1 5 5  0  0 0 0 0 0 0 | 1 * * * *
ooo3ooo3xox ...&#x   4 1  4 |  6  4  4  4  6 |  4  0  6  4  6  6  4  0 | 1 0  4  0  6  4  0  4  0 1 0 | 0 1 0  4  0 1 0 1 0 0 | * 5 * * *
... ooo3xox3ooo&#x   6 1  6 | 12  6  6  6 12 |  4  4 12  6 12 12  4  4 | 0 1  4  4 12  4  4  4  4 0 1 | 0 0 1  4  4 0 1 0 1 0 | * * 5 * *
o.o3o.o3x.x3o.o&#x  10 0 10 | 30  0 10  0 30 | 20 10  0  0 30  0 20 10 | 5 5  0  0  0 20 10  0  0 5 5 | 1 0 0  0  0 5 5 0 0 1 | * * * 1 *
.oo3.oo3.ox3.oo&#x   0 1 10 |  0  0  0 10 30 |  0  0  0  0  0 30 20 10 | 0 0  0  0  0  0  0 20 10 5 5 | 0 0 0  0  0 0 0 5 5 1 | * * * * 1

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