Acronym pentarin
Name tesseract atop rectified tesseract
Circumradius sqrt[(55+28 sqrt(2))/47] = 1.418705
Confer
general polytopal classes:
segmentopeta   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

oo3oo3oo3ox4xo&#x   → height = sqrt[8 sqrt(2)-9]/2   = 0.760544
(pent || rin)

o.3o.3o.3o.4o.    | 32  * |  5   5   0 | 10  10  5   0  0 | 10  10 10   0  0 |  5   5 10  0  0 | 1  1  5 0
.o3.o3.o3.o4.o    |  * 80 |  0   2   8 |  0   8  1  12  4 |  0  12  4   8  6 |  0   8  6  2  4 | 0  2  4 1
------------------+-------+------------+------------------+------------------+-----------------+----------
.. .. .. .. x.    |  2  0 | 80   *   * |  4   0  1   0  0 |  6   0  4   0  0 |  4   0  6  0  0 | 1  0  4 0
oo3oo3oo3oo4oo&#x |  1  1 |  * 160   * |  0   4  1   0  0 |  0   6  4   0  0 |  0   4  6  0  0 | 0  1  4 0
.. .. .. .x ..    |  0  2 |  *   * 320 |  0   1  0   3  1 |  0   3  1   3  3 |  0   3  3  1  3 | 0  1  3 1
------------------+-------+------------+------------------+------------------+-----------------+----------
.. .. .. o.4x.    |  4  0 |  4   0   0 | 80   *  *   *  * |  3   0  1   0  0 |  3   0  3  0  0 | 1  0  3 0
.. .. .. ox ..&#x |  1  2 |  0   2   1 |  * 320  *   *  * |  0   3  1   0  0 |  0   3  3  0  0 | 0  1  3 0
.. .. .. .. xo&#x |  2  1 |  1   2   0 |  *   * 80   *  *   0   0  4   0  0 |  0   0  6  0  0 | 0  0  4 0
.. .. .o3.x ..    |  0  3 |  0   0   3 |  *   *  * 320  * |  0   1  0   2  1 |  0   2  1  1  2 | 0  1  2 1
.. .. .. .x4.o    |  0  4 |  0   0   4 |  *   *  *   * 80 |  0   0  1   0  3 |  0   0  3  0  3 | 0  0  3 1
------------------+-------+------------+------------------+------------------+-----------------+----------
.. .. o.3o.4x.      8  0 | 12   0   0 |  6   0  0   0  0 | 40   *  *   *  * |  2   0  1  0  0 | 1  0  2 0
.. .. oo3ox ..&#x   1  3 |  0   3   3 |  0   3  0   1  0 |  * 320  *   *  * |  0   2  1  0  0 | 0  1  2 0
.. .. .. ox4xo&#x   4  4 |  4   8   4 |  1   4  4   0  1 |  *   * 80   *  * |  0   0  3  0  0 | 0  0  3 0
.. .o3.o3.x ..      0  4 |  0   0   6 |  0   0  0   4  0 |  *   *  * 160  * |  0   1  0  1  1 | 0  1  1 1
.. .. .o3.x4.o      0 12 |  0   0  24 |  0   0  0   8  6 |  *   *  *   * 40 |  0   0  1  0  2 | 0  0  2 1
------------------+-------+------------+------------------+------------------+-----------------+----------
.. o.3o.3o.4x.     16  0 | 32   0   0 | 24   0  0   0  0 |  8   0  0   0  0 | 10   *  *  *  * | 1  0  1 0
.. oo3oo3ox ..&#x   1  4 |  0   4   6 |  0   6  0   4  0 |  0   4  0   1  0 |  * 160  *  *  * | 0  1  1 0
.. .. oo3ox4xo&#x   8 12 | 12  24  24 |  6  24 12   8  6 |  1   8  6   0  1 |  *   * 40  *  * | 0  0  2 0
.o3.o3.o3.x ..      0  5 |  0   0  10 |  0   0  0  10  0 |  0   0  0   5  0 |  *   *  * 32  * | 0  1  0 1
.. .o3.o3.x4.o      0 32 |  0   0  96 |  0   0  0  64 24 |  0   0  0  16  8 |  *   *  *  * 10 | 0  0  1 1
------------------+-------+------------+------------------+------------------+-----------------+----------
o.3o.3o.3o.4x.     32  0 | 80   0   0 | 80   0  0   0  0 | 40   0  0   0  0 | 10   0  0  0  0 | 1  *  * *
oo3oo3oo3ox ..&#x   1  5 |  0   5  10 |  0  10  0  10  0 |  0  10  0   5  0 |  0   5  0  1  0 | * 32  * *
.. oo3oo3ox4xo&#x  16 32 | 32  64  96 | 24  96 32  64 24 |  8  64 24  16  8 |  1  16  8  0  1 | *  * 10 *
.o3.o3.o3.x4.o      0 80 |  0   0 320 |  0   0  0 320 80 |  0   0  0 160 40 |  0   0  0 32 10 | *  *  * 1

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