Acronym penpal rappip
Name penp atop alternate rappip,
dihin prism
Circumradius sqrt(7/8) = 0.935414
Lace city
in approx. ASCII-art
l   O  		-- xx oo3ox3oo&#x = octpyp
       
  t   T		-- xx xo3oo3ox&#x = alt. hexip

    \   \
     \   +-- x o3x3o3o = rappip
      +----- x o3o3o3x = inv. penp

where:
l = x o3o3o (line)
t = x x3o3o (tepe)
O = x o3x3o (ope)
T = x o3o3x (inv. tepe)
Face vector 30, 155, 330, 320, 139, 24
Confer
uniform relative:
hinnip  
segmentopeta:
rappyp  
general polytopal classes:
segmentopeta   lace simplices  

Incidence matrix according to Dynkin symbol

xx oo3ox3oo3xo&#x   → height = sqrt(2/5) = 0.632456
(penp || alt. rappip)

o. o.3o.3o.3o.    | 10  * | 1  4  6  0  0 |  4  6  6  12 12  0  0  0 |  6  4 12 12  4  4 12  6  0  0  0  0 | 4 1  4  4 12  6  1  4  4 0 0 0 | 1 1  4 4 1 0
.o .o3.o3.o3.o    |  * 20 | 0  0  3  1  6 |  0  0  3  12  3  6  3  6 |  0  0 12  3  6  6  6  1  3  6  3  2 | 0 0  6  6  6  1  3  3  2 3 2 1 | 0 3  3 2 1 1
------------------+-------+---------------+--------------------------+-------------------------------------+--------------------------------+-------------
x. .. .. .. ..    |  2  0 | 5  *  *  *  *   4  0  6   0  0  0  0  0 |  6  0 12 12  0  0  0  0  0  0  0  0 | 4 0  4  4 12  6  0  0  0 0 0 0 | 1 1  4 4 0 0
.. .. .. .. x.    |  2  0 | * 20  *  *  * |  1  3  0   0  3  0  0  0 |  3  3  0  3  0  0  3  3  0  0  0  0 | 3 1  0  0  3  3  0  1  3 0 0 0 | 1 0  1 3 1 0
oo oo3oo3oo3oo&#x |  1  1 | *  * 60  *  * |  0  0  1   4  2  0  0  0 |  0  0  4  2  2  2  4  1  0  0  0  0 | 0 0  2  2  4  1  1  2  2 0 0 0 | 0 1  2 2 1 0
.x .. .. .. ..    |  0  2 | *  *  * 10  *   0  0  3   0  0  6  0  0 |  0  0 12  3  0  0  0  0  3  6  0  0 | 0 0  6  6  6  1  0  0  0 3 2 0 | 0 3  3 2 0 1
.. .. .x .. ..    |  0  2 | *  *  *  * 60 |  0  0  0   2  0  1  1  2 |  0  0  2  0  2  2  1  0  1  2  2  1 | 0 0  2  2  1  0  2  1  1 2 1 1 | 0 2  1 1 1 1
------------------+-------+---------------+--------------------------+-------------------------------------+--------------------------------+-------------
x. .. .. .. x.    |  4  0 | 2  2  0  0  0 | 10  *  *   *  *  *  *  *   3  0  0  3  0  0  0  0  0  0  0  0 | 3 0  0  0  3  3  0  0  0 0 0 0 | 1 0  1 3 0 0
.. .. .. o.3x.    |  3  0 | 0  3  0  0  0 |  * 20  *   *  *  *  *  * |  1  2  0  0  0  0  0  1  0  0  0  0 | 2 1  0  0  0  1  0  0  2 0 0 0 | 1 0  0 2 1 0
xx .. .. .. ..&#x |  2  2 | 1  0  2  1  0 |  *  * 30   *  *  *  *  *   0  0  4  2  0  0  0  0  0  0  0  0 | 0 0  2  2  4  1  0  0  0 0 0 0 | 0 1  2 2 0 0
.. .. ox .. ..&#x |  1  2 | 0  0  2  0  1 |  *  *  * 120  *  *  *  * |  0  0  1  0  1  1  1  0  0  0  0  0 | 0 0  1  1  1  0  1  1  1 0 0 0 | 0 1  1 1 1 0
.. .. .. .. xo&#x |  2  1 | 0  1  2  0  0 |  *  *  *   * 60  *  *  * |  0  0  0  1  0  0  2  1  0  0  0  0 | 0 0  0  0  2  1  0  1  2 0 0 0 | 0 0  1 2 1 0
.x .. .x .. ..    |  0  4 | 0  0  0  2  2 |  *  *  *   *  * 30  *  * |  0  0  2  0  0  0  0  0  1  2  0  0 | 0 0  2  2  1  0  0  0  0 2 1 0 | 0 2  1 1 0 1
.. .o3.x .. ..    |  0  3 | 0  0  0  0  3 |  *  *  *   *  *  * 20  * |  0  0  0  0  2  0  0  0  1  0  2  0 | 0 0  2  0  0  0  2  1  0 2 0 1 | 0 2  1 0 1 1
.. .. .x3.o ..    |  0  3 | 0  0  0  0  3 |  *  *  *   *  *  *  * 40 |  0  0  0  0  0  1  0  0  0  1  1  1 | 0 0  0  1  0  0  1  0  1 1 1 1 | 0 1  0 1 1 1
------------------+-------+---------------+--------------------------+-------------------------------------+--------------------------------+-------------
x. .. .. o.3x.      6  0 | 3  6  0  0  0 |  3  2  0   0  0  0  0  0 | 10  *  *  *  *  *  *  *  *  *  *  * | 2 0  0  0  0  1  0  0  0 0 0 0 | 1 0  0 2 0 0
.. .. o.3o.3x.      4  0 | 0  6  0  0  0 |  0  4  0   0  0  0  0  0 |  * 10  *  *  *  *  *  *  *  *  *  * | 1 1  0  0  0  0  0  0  1 0 0 0 | 1 0  0 1 1 0
xx .. ox .. ..&#x   2  4 | 1  0  4  2  2 |  0  0  2   2  0  1  0  0 |  *  * 60  *  *  *  *  *  *  *  *  * | 0 0  1  1  1  0  0  0  0 0 0 0 | 0 1  1 1 0 0
xx .. .. .. xo&#x   4  2 | 2  2  4  1  0 |  1  0  2   0  2  0  0  0 |  *  *  * 30  *  *  *  *  *  *  *  * | 0 0  0  0  2  1  0  0  0 0 0 0 | 0 0  1 2 0 0
.. oo3ox .. ..&#x   1  3 | 0  0  3  0  3 |  0  0  0   3  0  0  1  0 |  *  *  *  * 40  *  *  *  *  *  *  * | 0 0  1  0  0  0  1  1  0 0 0 0 | 0 1  1 0 1 0
.. .. ox3oo ..&#x   1  3 | 0  0  3  0  3 |  0  0  0   3  0  0  0  1 |  *  *  *  *  * 40  *  *  *  *  *  * | 0 0  0  1  0  0  1  0  1 0 0 0 | 0 1  0 1 1 0
.. .. ox .. xo&#x   2  2 | 0  1  4  0  1 |  0  0  0   2  2  0  0  0 |  *  *  *  *  *  * 60  *  *  *  *  * | 0 0  0  0  1  0  0  1  1 0 0 0 | 0 0  1 1 1 0
.. .. .. oo3xo&#x   3  1 | 0  3  3  0  0 |  0  1  0   0  3  0  0  0 |  *  *  *  *  *  *  * 20  *  *  *  * | 0 0  0  0  0  1  0  0  2 0 0 0 | 0 0  0 2 1 0
.x .o3.x .. ..      0  6 | 0  0  0  3  6 |  0  0  0   0  0  3  2  0 |  *  *  *  *  *  *  *  * 10  *  *  * | 0 0  2  0  0  0  0  0  0 2 0 0 | 0 2  1 0 0 1
.x .. .x3.o ..      0  6 | 0  0  0  3  6 |  0  0  0   0  0  3  0  2 |  *  *  *  *  *  *  *  *  * 20  *  * | 0 0  0  1  0  0  0  0  0 1 1 0 | 0 1  0 1 0 1
.. .o3.x3.o ..      0  6 | 0  0  0  0 12 |  0  0  0   0  0  0  4  4 |  *  *  *  *  *  *  *  *  *  * 10  * | 0 0  0  0  0  0  1  0  0 1 0 1 | 0 1  0 0 1 1
.. .. .x3.o3.o      0  4 | 0  0  0  0  6 |  0  0  0   0  0  0  0  4 |  *  *  *  *  *  *  *  *  *  *  * 10 | 0 0  0  0  0  0  0  0  1 0 1 1 | 0 0  0 1 1 1
------------------+-------+---------------+--------------------------+-------------------------------------+--------------------------------+-------------
x. .. o.3o.3x.      8  0 | 4 12  0  0  0 |  6  8  0   0  0  0  0  0 |  4  2  0  0  0  0  0  0  0  0  0  0 | 5 *  *  *  *  *  *  *  * * * * | 1 0  0 1 0 0
.. o.3o.3o.3x.      5  0 | 0 10  0  0  0 |  0 10  0   0  0  0  0  0 |  0  5  0  0  0  0  0  0  0  0  0  0 | * 2  *  *  *  *  *  *  * * * * | 1 0  0 0 1 0
xx oo3ox .. ..&#x   2  6 | 1  0  6  3  6 |  0  0  3   6  0  3  2  0 |  0  0  3  0  2  0  0  0  1  0  0  0 | * * 20  *  *  *  *  *  * * * * | 0 1  1 0 0 0
xx .. ox3oo ..&#x   2  6 | 1  0  6  3  6 |  0  0  3   6  0  3  0  2 |  0  0  3  0  0  2  0  0  0  1  0  0 | * *  * 20  *  *  *  *  * * * * | 0 1  0 1 0 0
xx .. ox .. xo&#x   4  4 | 2  2  8  2  2 |  1  0  4   4  4  1  0  0 |  0  0  2  2  0  0  2  0  0  0  0  0 | * *  *  * 30  *  *  *  * * * * | 0 0  1 1 0 0
xx .. .. oo3xo&#x   6  2 | 3  6  6  1  0 |  3  2  3   0  6  0  0  0 |  1  0  0  3  0  0  0  2  0  0  0  0 | * *  *  *  * 10  *  *  * * * * | 0 0  0 2 0 0
.. oo3ox3oo ..&#x   1  6 | 0  0  6  0 12 |  0  0  0  12  0  0  4  4 |  0  0  0  0  4  4  0  0  0  0  1  0 | * *  *  *  *  * 10  *  * * * * | 0 1  0 0 1 0
.. oo3ox .. xo&#x   2  3 | 0  1  6  0  3 |  0  0  0   6  3  0  1  0 |  0  0  0  0  2  0  3  0  0  0  0  0 | * *  *  *  *  *  * 20  * * * * | 0 0  1 0 1 0
.. .. ox3oo3xo&#x   4  4 | 0  6 12  0  6 |  0  4  0  12 12  0  0  4 |  0  1  0  0  0  4  6  4  0  0  0  1 | * *  *  *  *  *  *  * 10 * * * | 0 0  0 1 1 0
.x .o3.x3.o ..      0 12 | 0  0  0  6 24 |  0  0  0   0  0 12  8  8 |  0  0  0  0  0  0  0  0  4  4  2  0 | * *  *  *  *  *  *  *  * 5 * * | 0 1  0 0 0 1
.x .. .x3.o3.o      0  8 | 0  0  0  4 12 |  0  0  0   0  0  6  0  8 |  0  0  0  0  0  0  0  0  0  4  0  2 | * *  *  *  *  *  *  *  * * 5 * | 0 0  0 1 0 1
.. .o3.x3.o3.o      0 10 | 0  0  0  0 30 |  0  0  0   0  0  0 10 20 |  0  0  0  0  0  0  0  0  0  0  5  5 | * *  *  *  *  *  *  *  * * * 2 | 0 0  0 0 1 1
------------------+-------+---------------+--------------------------+-------------------------------------+--------------------------------+-------------
x. o.3o.3o.3x.     10  0 | 5 20  0  0  0 | 10 20  0   0  0  0  0  0 | 10 10  0  0  0  0  0  0  0  0  0  0 | 5 2  0  0  0  0  0  0  0 0 0 0 | 1 *  * * * *
xx oo3ox3oo ..&#x   2 12 | 1  0 12  6 24 |  0  0  6  24  0 12  8  8 |  0  0 12  0  8  8  0  0  4  4  2  0 | 0 0  4  4  0  0  2  0  0 1 0 0 | * 5  * * * *
xx oo3ox .. xo&#x   4  6 | 2  2 12  3  6 |  1  0  6  12  6  3  2  0 |  0  0  6  3  4  0  6  0  1  0  0  0 | 0 0  2  0  3  0  0  2  0 0 0 0 | * * 10 * * *
xx .. ox3oo3xo&#x   8  8 | 4 12 24  4 12 |  6  8 12  24 24  6  0  8 |  4  2 12 12  0  8 12  8  0  4  0  2 | 1 0  0  4  6  4  0  0  2 0 1 0 | * *  * 5 * *
.. oo3ox3oo3xo&#x   5 10 | 0 10 30  0 30 |  0 10  0  60 30  0 10 20 |  0  5  0  0 20 20 30 10  0  0  5  5 | 0 1  0  0  0  0  5 10  5 0 0 1 | * *  * * 2 *
.x .o3.x3.o3.o      0 20 | 0  0  0 10 60 |  0  0  0   0  0 30 20 40 |  0  0  0  0  0  0  0  0 10 20 10 10 | 0 0  0  0  0  0  0  0  0 5 5 2 | * *  * * * 1

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