Acronym trapip (old: trapedippip)
Name triangle pentagonal-prism duoprism,
triangle-pentagon duoprismatic prism
Circumradius sqrt[(65+6 sqrt(5))/60] = 1.143215
Confer
more general:
n,m-dippip   3,n-dippip   5,n-dippip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol


x x3o x5o

. . . . . | 30 |  1  2  2 |  2  2  1  4 1 | 1  4 1  2 2 | 2 2 1
----------+----+----------+---------------+-------------+------
x . . . . |  2 | 15  *  * |  2  2  0  0 0 | 1  4 1  0 0 | 2 2 0
. x . . . |  2 |  * 30  * |  1  0  1  2 0 | 1  2 0  2 1 | 2 1 1
. . . x . |  2 |  *  * 30 |  0  1  0  2 1 | 0  2 1  1 2 | 1 2 1
----------+----+----------+---------------+-------------+------
x x . . . |  4 |  2  2  0 | 15  *  *  * * | 1  2 0  0 0 | 2 1 0
x . . x . |  4 |  2  0  2 |  * 15  *  * * | 0  2 1  0 0 | 1 2 0
. x3o . . |  3 |  0  3  0 |  *  * 10  * * | 1  0 0  2 0 | 2 0 1
. x . x . |  4 |  0  2  2 |  *  *  * 30 * | 0  1 0  1 1 | 1 1 1
. . . x5o |  5 |  0  0  5 |  *  *  *  * 6 | 0  0 1  0 2 | 0 2 1
----------+----+----------+---------------+-------------+------
x x3o . .   6 |  3  6  0 |  3  0  2  0 0 | 5  * *  * * | 2 0 0
x x . x .   8 |  4  4  4 |  2  2  0  2 0 | * 15 *  * * | 1 1 0
x . . x5o  10 |  5  0 10 |  0  5  0  0 2 | *  * 3  * * | 0 2 0
. x3o x .   6 |  0  6  3 |  0  0  2  3 0 | *  * * 10 * | 1 0 1
. x . x5o  10 |  0  5 10 |  0  0  0  5 2 | *  * *  * 6 | 0 1 1
----------+----+----------+---------------+-------------+------
x x3o x .  12 |  6 12  6 |  6  3  4  6 0 | 2  3 0  2 0 | 5 * *
x x . x5o  20 | 10 10 20 |  5 10  0 10 4 | 0  5 2  0 2 | * 3 *
. x3o x5o  15 |  0 15 15 |  0  0  5 15 3 | 0  0 0  5 3 | * * 2

xx3oo xx5oo&#x   → height = 1
(trapedip || trapedip)

o.3o. o.5o.    | 15  * |  2  2  1  0  0 | 1  4 1  2  2 0  0 0 | 2 2 1  4 1 0 0 | 1 2 2 0
.o3.o .o5.o    |  * 15 |  0  0  1  2  2 | 0  0 0  2  2 1  4 1 | 0 0 1  4 1 2 2 | 0 2 2 1
---------------+-------+----------------+---------------------+----------------+--------
x. .. .. ..    |  2  0 | 15  *  *  *  * | 1  2 0  1  0 0  0 0 | 2 1 1  2 0 0 0 | 1 2 1 0
.. .. x. ..    |  2  0 |  * 15  *  *  * | 0  2 1  0  1 0  0 0 | 1 2 0  2 1 0 0 | 1 1 2 0
oo3oo oo5oo&#x |  1  1 |  *  * 15  *  * | 0  0 0  2  2 0  0 0 | 0 0 1  4 1 0 0 | 0 2 2 0
.x .. .. ..    |  0  2 |  *  *  * 15  * | 0  0 0  1  0 1  2 0 | 0 0 1  2 0 2 1 | 0 2 1 1
.. .. .x ..    |  0  2 |  *  *  *  * 15 | 0  0 0  0  1 0  2 1 | 0 0 0  2 1 1 2 | 0 1 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. .. ..    |  3  0 |  3  0  0  0  0 | 5  * *  *  * *  * * | 2 0 1  0 0 0 0 | 1 2 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 15 *  *  * *  * * | 1 1 0  1 0 0 0 | 1 1 1 0
.. .. x.5o.    |  5  0 |  0  5  0  0  0 | *  * 3  *  * *  * * | 0 2 0  0 1 0 0 | 1 0 2 0
xx .. .. ..&#x |  2  2 |  1  0  2  1  0 | *  * * 15  * *  * * | 0 0 1  2 0 0 0 | 0 2 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  * 15 *  * * | 0 0 0  2 1 0 0 | 0 1 2 0
.x3.o .. ..    |  0  3 |  0  0  0  3  0 | *  * *  *  * 5  * * | 0 0 1  0 0 2 0 | 0 2 0 1
.x .. .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  * * 15 * | 0 0 0  1 0 1 1 | 0 1 1 1
.. .. .x5.o    |  0  5 |  0  0  0  0  5 | *  * *  *  * *  * 3 | 0 0 0  0 1 0 2 | 0 0 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x. ..      6  0 |  6  3  0  0  0 | 2  3 0  0  0 0  0 0 | 5 * *  * * * * | 1 1 0 0
x. .. x.5o.     10  0 |  5 10  0  0  0 | 0  5 2  0  0 0  0 0 | * 3 *  * * * * | 1 0 1 0
xx3oo .. ..&#x   3  3 |  3  0  3  3  0 | 1  0 0  3  0 1  0 0 | * * 5  * * * * | 0 2 0 0
xx .. xx ..&#x   4  4 |  2  2  4  2  2 | 0  1 0  2  2 0  1 0 | * * * 15 * * * | 0 1 1 0
.. .. xx5oo&#x   5  5 |  0  5  5  0  5 | 0  0 1  0  5 0  0 1 | * * *  * 3 * * | 0 0 2 0
.x3.o .x ..      0  6 |  0  0  0  6  3 | 0  0 0  0  0 2  3 0 | * * *  * * 5 * | 0 1 0 1
.x .. .x5.o      0 10 |  0  0  0  5 10 | 0  0 0  0  0 0  5 2 | * * *  * * * 3 | 0 0 1 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x.5o.     15  0 | 15 15  0  0  0 | 5 15 3  0  0 0  0 0 | 5 3 0  0 0 0 0 | 1 * * *
xx3oo xx ..&#x   6  6 |  6  3  6  6  3 | 2  3 0  6  3 2  3 0 | 1 0 2  3 0 1 0 | * 5 * *
xx .. xx5oo&#x  10 10 |  5 10 10  5 10 | 0  5 2  5 10 0  5 2 | 0 1 0  5 2 0 1 | * * 3 *
.x3.o .x5.o      0 15 |  0  0  0 15 15 | 0  0 0  0  0 5 15 3 | 0 0 0  0 0 5 3 | * * * 1

ox xx xx5oo&#x   → height = sqrt(3)/2 = 0.866025
(pip || squipdip)

o. o. o.5o.    | 10  * | 1  2  2  0  0  0 | 2 1  1  2  4 0  0  0 0 | 1 1  2  4 2 0 0 0 | 2 1 2 0
.o .o .o5.o    |  * 20 | 0  0  1  1  1  2 | 0 0  1  1  2 1  2  2 1 | 0 1  2  2 1 2 1 1 | 2 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. .. ..    |  2  0 | 5  *  *  *  *  * | 2 0  0  2  0 0  0  0 0 | 1 1  0  4 0 0 0 0 | 2 0 2 0
.. .. x. ..    |  2  0 | * 10  *  *  *  * | 1 1  0  0  2 0  0  0 0 | 1 0  1  2 2 0 0 0 | 1 1 2 0
oo oo oo5oo&#x |  1  1 | *  * 20  *  *  * | 0 0  1  1  2 0  0  0 0 | 0 1  2  2 1 0 0 0 | 2 1 1 0
.x .. .. ..    |  0  2 | *  *  * 10  *  * | 0 0  1  0  0 1  2  0 0 | 0 1  2  0 0 2 1 0 | 2 1 0 1
.. .x .. ..    |  0  2 | *  *  *  * 10  * | 0 0  0  1  0 1  0  2 0 | 0 1  0  2 0 2 0 1 | 2 0 1 1
.. .. .x ..    |  0  2 | *  *  *  *  * 20 | 0 0  0  0  1 0  1  1 1 | 0 0  1  1 1 1 1 1 | 1 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. x. ..    |  4  0 | 2  2  0  0  0  0 | 5 *  *  *  * *  *  * * | 1 0  0  2 0 0 0 0 | 1 0 2 0
.. .. x.5o.    |  5  0 | 0  5  0  0  0  0 | * 2  *  *  * *  *  * * | 1 0  0  0 2 0 0 0 | 0 1 2 0
ox .. .. ..&#x |  1  2 | 0  0  2  1  0  0 | * * 10  *  * *  *  * * | 0 1  2  0 0 0 0 0 | 2 1 0 0
.. xx .. ..&#x |  2  2 | 1  0  2  0  1  0 | * *  * 10  * *  *  * * | 0 1  0  2 0 0 0 0 | 2 0 1 0
.. .. xx ..&#x |  2  2 | 0  1  2  0  0  1 | * *  *  * 20 *  *  * * | 0 0  1  1 1 0 0 0 | 1 1 1 0
.x .x .. ..    |  0  4 | 0  0  0  2  2  0 | * *  *  *  * 5  *  * * | 0 1  0  0 0 2 0 0 | 2 0 0 1
.x .. .x ..    |  0  4 | 0  0  0  2  0  2 | * *  *  *  * * 10  * * | 0 0  1  0 0 1 1 0 | 1 1 0 1
.. .x .x ..    |  0  4 | 0  0  0  0  2  2 | * *  *  *  * *  * 10 * | 0 0  0  1 0 1 0 1 | 1 0 1 1
.. .. .x5.o    |  0  5 | 0  0  0  0  0  5 | * *  *  *  * *  *  * 4 | 0 0  0  0 1 0 1 1 | 0 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. x.5o.     10  0 | 5 10  0  0  0  0 | 5 2  0  0  0 0  0  0 0 | 1 *  *  * * * * * | 0 0 2 0
ox xx .. ..&#x   2  4 | 1  0  4  2  2  0 | 0 0  2  2  0 1  0  0 0 | * 5  *  * * * * * | 2 0 0 0
ox .. xx ..&#x   2  4 | 0  1  4  2  0  2 | 0 0  2  0  2 0  1  0 0 | * * 10  * * * * * | 1 1 0 0
.. xx xx ..&#x   4  4 | 2  2  4  0  2  2 | 1 0  0  2  2 0  0  1 0 | * *  * 10 * * * * | 1 0 1 0
.. .. xx5oo&#x   5  5 | 0  5  5  0  0  5 | 0 1  0  0  5 0  0  0 1 | * *  *  * 4 * * * | 0 1 1 0
.x .x .x ..      0  8 | 0  0  0  4  4  4 | 0 0  0  0  0 2  2  2 0 | * *  *  * * 5 * * | 1 0 0 1
.x .. .x5.o      0 10 | 0  0  0  5  0 10 | 0 0  0  0  0 0  5  0 2 | * *  *  * * * 2 * | 0 1 0 1
.. .x .x5.o      0 10 | 0  0  0  0  5 10 | 0 0  0  0  0 0  0  5 2 | * *  *  * * * * 2 | 0 0 1 1
---------------+-------+------------------+------------------------+-------------------+--------
ox xx xx ..&#x   4  8 | 2  2  8  4  4  4 | 1 0  4  4  4 2  2  2 0 | 0 2  2  2 0 1 0 0 | 5 * * *
ox .. xx5oo&#x   5 10 | 0  5 10  5  0 10 | 0 1  5  0 10 0  5  0 2 | 0 0  5  0 2 0 1 0 | * 2 * *
.. xx xx5oo&#x  10 10 | 5 10 10  0  5 10 | 5 2  0  5 10 0  0  5 2 | 1 0  0  5 2 0 0 1 | * * 2 *
.x .x .x5.o      0 20 | 0  0  0 10 10 20 | 0 0  0  0  0 5 10 10 4 | 0 0  0  0 0 5 2 2 | * * * 1

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