Acronym penalpenp
Name pentachoron atop inverted pentachoral-prism,
pen-first cap of jak
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art
p  
  d
p  

where:
p = x3o3o3o (pen)
d = o3o3o3x (dual pen)
Confer
uniform relative:
jak  
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

xo ox3oo3oo3xo&#xt   → height = sqrt(3/20) = 0.387298
(penp || dual pen)

o. o.3o.3o.3o.    | 10 * | 1  4  4  0 |  4  6  4  6 12  0 |  6  4  6 12  4 12 12 0 | 4 1  4 12 12  1  4  6  4 0 | 1 1  4  6 4 1
.o .o3.o3.o3.o    |  * 5 | 0  0  8  4 |  0  0  4 24 12  6 |  0  0 12  6 24 24  8 4 | 0 0 12 12  4  8 12  8  2 1 | 0 4  6  4 1 2
------------------+------+------------+-------------------+------------------------+----------------------------+--------------
x. .. .. .. ..    |  2 0 | 5  *  *  * |  4  0  4  0  0  0 |  6  0  6 12  0  0  0 0 | 4 0  4 12 12  0  0  0  0 0 | 1 1  4  6 4 0
.. .. .. .. x.    |  2 0 | * 20  *  * |  1  3  0  0  3  0 |  3  3  0  3  0  3  6 0 | 3 1  0  3  6  0  1  3  3 0 | 1 0  1  3 3 1
oo oo3oo3oo3oo&#x |  1 1 | *  * 40  * |  0  0  1  3  3  0 |  0  0  3  3  3  6  3 0 | 0 0  3  6  3  1  3  3  1 0 | 0 1  3  3 1 1
.. .x .. .. ..    |  0 2 | *  *  * 10 |  0  0  0  6  0  3 |  0  0  3  0 12  6  0 3 | 0 0  6  3  0  6  6  2  0 1 | 0 3  3  1 0 2
------------------+------+------------+-------------------+------------------------+----------------------------+--------------
x. .. .. .. x.    |  4 0 | 2  2  0  0 | 10  *  *  *  *  * |  3  0  0  3  0  0  0 0 | 3 0  0  3  6  0  0  0  0 0 | 1 0  1  3 3 0
.. .. .. o.3x.    |  3 0 | 0  3  0  0 |  * 20  *  *  *  * |  1  2  0  0  0  0  2 0 | 2 1  0  0  2  0  0  1  2 0 | 1 0  0  1 2 1
xo .. .. .. ..&#x |  2 1 | 1  0  2  0 |  *  * 20  *  *  * |  0  0  3  3  0  0  0 0 | 0 0  3  6  3  0  0  0  0 0 | 0 1  3  3 1 0
.. ox .. .. ..&#x |  1 2 | 0  0  2  1 |  *  *  * 60  *  * |  0  0  1  0  2  2  0 0 | 0 0  2  2  0  1  2  1  0 0 | 0 1  2  1 0 1
.. .. .. .. xo&#x |  2 1 | 0  1  2  0 |  *  *  *  * 60  * |  0  0  0  1  0  2  2 0 | 0 0  0  2  2  0  1  2  1 0 | 0 0  1  2 1 1
.. .x3.o .. ..    |  0 3 | 0  0  0  3 |  *  *  *  *  * 10 |  0  0  0  0  4  0  0 2 | 0 0  2  0  0  4  2  0  0 1 | 0 2  1  0 0 2
------------------+------+------------+-------------------+------------------------+----------------------------+--------------
x. .. .. o.3x.      6 0 | 3  6  0  0 |  3  2  0  0  0  0 | 10  *  *  *  *  *  * * | 2 0  0  0  2  0  0  0  0 0 | 1 0  0  1 2 0
.. .. o.3o.3x.      4 0 | 0  6  0  0 |  0  4  0  0  0  0 |  * 10  *  *  *  *  * * | 1 1  0  0  0  0  0  0  1 0 | 1 0  0  0 1 1
xo ox .. .. ..&#x   2 2 | 1  0  4  1 |  0  0  2  2  0  0 |  *  * 30  *  *  *  * * | 0 0  2  2  0  0  0  0  0 0 | 0 1  2  1 0 0
xo .. .. .. xo&#x   4 1 | 2  2  4  0 |  1  0  2  0  2  0 |  *  *  * 30  *  *  * * | 0 0  0  2  2  0  0  0  0 0 | 0 0  1  2 1 0
.. ox3oo .. ..&#x   1 3 | 0  0  3  3 |  0  0  0  3  0  1 |  *  *  *  * 40  *  * * | 0 0  1  0  0  1  1  0  0 0 | 0 1  1  0 0 1
.. ox .. .. xo&#x   2 2 | 0  1  4  1 |  0  0  0  2  2  0 |  *  *  *  *  * 60  * * | 0 0  0  1  0  0  1  1  0 0 | 0 0  1  1 0 1
.. .. .. oo3xo&#x   3 1 | 0  3  3  0 |  0  1  0  0  3  0 |  *  *  *  *  *  * 40 * | 0 0  0  0  1  0  0  1  1 0 | 0 0  0  1 1 1
.. .x3.o3.o ..      0 4 | 0  0  0  6 |  0  0  0  0  0  4 |  *  *  *  *  *  *  * 5 | 0 0  0  0  0  2  0  0  0 1 | 0 1  0  0 0 2
------------------+------+------------+-------------------+------------------------+----------------------------+--------------
x. .. o.3o.3x.      8 0 | 4 12  0  0 |  6  8  0  0  0  0 |  4  2  0  0  0  0  0 0 | 5 *  *  *  *  *  *  *  * * | 1 0  0  0 1 0
.. o.3o.3o.3x.      5 0 | 0 10  0  0 |  0 10  0  0  0  0 |  0  5  0  0  0  0  0 0 | * 2  *  *  *  *  *  *  * * | 1 0  0  0 0 1
xo ox3oo .. ..&#x   2 3 | 1  0  6  3 |  0  0  3  6  0  1 |  0  0  3  0  2  0  0 0 | * * 20  *  *  *  *  *  * * | 0 1  1  0 0 0
xo ox .. .. xo&#x   4 2 | 2  2  8  1 |  1  0  4  4  4  0 |  0  0  2  2  0  2  0 0 | * *  * 30  *  *  *  *  * * | 0 0  1  1 0 0
xo .. .. oo3xo&#x   6 1 | 3  6  6  0 |  3  2  3  0  6  0 |  1  0  0  3  0  0  2 0 | * *  *  * 20  *  *  *  * * | 0 0  0  1 1 0
.. ox3oo3oo ..&#x   1 4 | 0  0  4  6 |  0  0  0  6  0  4 |  0  0  0  0  4  0  0 1 | * *  *  *  * 10  *  *  * * | 0 1  0  0 0 1
.. ox3oo .. xo&#x   2 3 | 0  1  6  3 |  0  0  0  6  3  1 |  0  0  0  0  2  3  0 0 | * *  *  *  *  * 20  *  * * | 0 0  1  0 0 1
.. ox .. oo3xo&#x   3 2 | 0  3  6  1 |  0  1  0  3  6  0 |  0  0  0  0  0  3  2 0 | * *  *  *  *  *  * 20  * * | 0 0  0  1 0 1
.. .. oo3oo3xo&#x   4 1 | 0  6  4  0 |  0  4  0  0  6  0 |  0  1  0  0  0  0  4 0 | * *  *  *  *  *  *  * 10 * | 0 0  0  0 1 1
.. .x3.o3.o3.o      0 5 | 0  0  0 10 |  0  0  0  0  0 10 |  0  0  0  0  0  0  0 5 | * *  *  *  *  *  *  *  * 1 | 0 0  0  0 0 2
------------------+------+------------+-------------------+------------------------+----------------------------+--------------
x. o.3o.3o.3x.     10 0 | 5 20  0  0 | 10 20  0  0  0  0 | 10 10  0  0  0  0  0 0 | 5 2  0  0  0  0  0  0  0 0 | 1 *  *  * * *
xo ox3oo3oo ..&#x   2 4 | 1  0  8  6 |  0  0  4 12  0  4 |  0  0  6  0  8  0  0 1 | 0 0  4  0  0  2  0  0  0 0 | * 5  *  * * *
xo ox3oo .. xo&#x   4 3 | 2  2 12  3 |  1  0  6 12  6  1 |  0  0  6  3  4  6  0 0 | 0 0  2  3  0  0  2  0  0 0 | * * 10  * * *
xo ox .. oo3xo&#x   6 2 | 3  6 12  1 |  3  2  6  6 12  0 |  1  0  3  6  0  6  4 0 | 0 0  0  3  2  0  0  2  0 0 | * *  * 10 * *
xo .. oo3oo3xo&#x   8 1 | 4 12  8  0 |  6  8  4  0 12  0 |  4  2  0  6  0  0  8 0 | 1 0  0  0  4  0  0  0  2 0 | * *  *  * 5 *
.. ox3oo3oo3xo&#x   5 5 | 0 10 20 10 |  0 10  0 30 30 10 |  0  5  0  0 20 30 20 5 | 0 1  0  0  0  5 10 10  5 1 | * *  *  * * 2

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