Acronym pecube
Name pentagon-cube duoprism
Circumradius sqrt[(25+2 sqrt(5))/20] = 1.213922
Confer
more general:
n,cube-dip   n,m-dippip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x5o o3o4x

. . . . . | 40 |  2  3 | 1  6  3 |  3  6 1 | 3 2
----------+----+-------+---------+---------+----
x . . . . |  2 | 40  * | 1  3  0 |  3  3 0 | 3 1
. . . . x |  2 |  * 60 | 0  2  2 |  1  4 1 | 2 2
----------+----+-------+---------+---------+----
x5o . . . |  5 |  5  0 | 8  *  * |  3  0 0 | 3 0
x . . . x |  4 |  2  2 | * 60  * |  1  2 0 | 2 1
. . . o4x |  4 |  0  4 | *  * 30 |  0  2 1 | 1 2
----------+----+-------+---------+---------+----
x5o . . x  10 | 10  5 | 2  5  0 | 12  * * | 2 0
x . . o4x   8 |  4  8 | 0  4  2 |  * 30 * | 1 1
. . o3o4x   8 |  0 12 | 0  0  6 |  *  * 5 | 0 2
----------+----+-------+---------+---------+----
x5o . o4x  20 | 20 20 | 4 20  5 |  4  5 0 | 6 *
x . o3o4x  16 |  8 24 | 0 12 12 |  0  6 2 | * 5

x x4o x5o

. . . . . | 40 |  1  2  2 |  2  2  1  4 1 | 1  4 1  2 2 | 2 2 1
----------+----+----------+---------------+-------------+------
x . . . . |  2 | 20  *  * |  2  2  0  0 0 | 1  4 1  0 0 | 2 2 0
. x . . . |  2 |  * 40  * |  1  0  1  2 0 | 1  2 0  2 1 | 2 1 1
. . . x . |  2 |  *  * 40 |  0  1  0  2 1 | 0  2 1  1 2 | 1 2 1
----------+----+----------+---------------+-------------+------
x x . . . |  4 |  2  2  0 | 20  *  *  * * | 1  2 0  0 0 | 2 1 0
x . . x . |  4 |  2  0  2 |  * 20  *  * * | 0  2 1  0 0 | 1 2 0
. x4o . . |  4 |  0  4  0 |  *  * 10  * * | 1  0 0  2 0 | 2 0 1
. x . x . |  4 |  0  2  2 |  *  *  * 40 * | 0  1 0  1 1 | 1 1 1
. . . x5o |  5 |  0  0  5 |  *  *  *  * 8 | 0  0 1  0 2 | 0 2 1
----------+----+----------+---------------+-------------+------
x x4o . .   8 |  4  8  0 |  4  0  2  0 0 | 5  * *  * * | 2 0 0
x x . x .   8 |  4  4  4 |  2  2  0  2 0 | * 20 *  * * | 1 1 0
x . . x5o  10 |  5  0 10 |  0  5  0  0 2 | *  * 4  * * | 0 2 0
. x4o x .   8 |  0  8  4 |  0  0  2  4 0 | *  * * 10 * | 1 0 1
. x . x5o  10 |  0  5 10 |  0  0  0  5 2 | *  * *  * 8 | 0 1 1
----------+----+----------+---------------+-------------+------
x x4o x .  16 |  8 16  8 |  8  4  4  8 0 | 2  4 0  2 0 | 5 * *
x x . x5o  20 | 10 10 20 |  5 10  0 10 4 | 0  5 2  0 2 | * 4 *
. x4o x5o  20 |  0 20 20 |  0  0  5 20 4 | 0  0 0  5 4 | * * 2

x x x x5o

. . . . . | 40 |  1  1  1  2 |  1  1  2  1  2  2 1 | 1  2  2 1  2 1 1 | 2 1 1 1
----------+----+-------------+---------------------+------------------+--------
x . . . . |  2 | 20  *  *  * |  1  1  2  0  0  0 0 | 1  2  2 1  0 0 0 | 2 1 1 0
. x . . . |  2 |  * 20  *  * |  1  0  0  1  2  0 0 | 1  2  0 0  2 1 0 | 2 1 0 1
. . x . . |  2 |  *  * 20  * |  0  1  0  1  0  2 0 | 1  0  2 0  2 0 1 | 2 0 1 1
. . . x . |  2 |  *  *  * 40 |  0  0  1  0  1  1 1 | 0  1  1 1  1 1 1 | 1 1 1 1
----------+----+-------------+---------------------+------------------+--------
x x . . . |  4 |  2  2  0  0 | 10  *  *  *  *  * * | 1  2  0 0  0 0 0 | 2 1 0 0
x . x . . |  4 |  2  0  2  0 |  * 10  *  *  *  * * | 1  0  2 0  0 0 0 | 2 0 1 0
x . . x . |  4 |  2  0  0  2 |  *  * 20  *  *  * * | 0  1  1 1  0 0 0 | 1 1 1 0
. x x . . |  4 |  0  2  2  0 |  *  *  * 10  *  * * | 1  0  0 0  2 0 0 | 2 0 0 1
. x . x . |  4 |  0  2  0  2 |  *  *  *  * 20  * * | 0  1  0 0  1 1 0 | 1 1 0 1
. . x x . |  4 |  0  0  2  2 |  *  *  *  *  * 20 * | 0  0  1 0  1 0 1 | 1 0 1 1
. . . x5o |  5 |  0  0  0  5 |  *  *  *  *  *  * 8 | 0  0  0 1  0 1 1 | 0 1 1 1
----------+----+-------------+---------------------+------------------+--------
x x x . .   8 |  4  4  4  0 |  2  2  0  2  0  0 0 | 5  *  * *  * * * | 2 0 0 0
x x . x .   8 |  4  4  0  4 |  2  0  2  0  2  0 0 | * 10  * *  * * * | 1 1 0 0
x . x x .   8 |  4  0  4  4 |  0  2  2  0  0  2 0 | *  * 10 *  * * * | 1 0 1 0
x . . x5o  10 |  5  0  0 10 |  0  0  5  0  0  0 2 | *  *  * 4  * * * | 0 1 1 0
. x x x .   8 |  0  4  4  4 |  0  0  0  2  2  2 0 | *  *  * * 10 * * | 1 0 0 1
. x . x5o  10 |  0  5  0 10 |  0  0  0  0  5  0 2 | *  *  * *  * 4 * | 0 1 0 1
. . x x5o  10 |  0  0  5 10 |  0  0  0  0  0  5 2 | *  *  * *  * * 4 | 0 0 1 1
----------+----+-------------+---------------------+------------------+--------
x x x x .  16 |  8  8  8  8 |  4  4  4  4  4  4 0 | 2  2  2 0  2 0 0 | 5 * * *
x x . x5o  20 | 10 10  0 20 |  5  0 10  0 10  0 4 | 0  5  0 2  0 2 0 | * 2 * *
x . x x5o  20 | 10  0 10 20 |  0  5 10  0  0 10 4 | 0  0  5 2  0 0 2 | * * 2 *
. x x x5o  20 |  0 10 10 20 |  0  0  0  5 10 10 4 | 0  0  0 0  5 2 2 | * * * 2

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