Acronym trapen
Name triangle - pentachoron duoprism,
vertex figure of broc
Circumradius sqrt(11/15) = 0.856349
Confer
more general:
n,pen-dip  
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

x3o x3o3o3o

. . . . . . | 15 |  2  4 | 1  8  6 |  4 12  4 |  6  8 1 | 4 2
------------+----+-------+---------+----------+---------+----
x . . . . . |  2 | 15  * | 1  4  0 |  4  6  0 |  6  4 0 | 4 1
. . x . . . |  2 |  * 30 | 0  2  3 |  1  6  3 |  3  6 1 | 3 2
------------+----+-------+---------+----------+---------+----
x3o . . . . |  3 |  3  0 | 5  *  *   4  0  0 |  6  0 0 | 4 0
x . x . . . |  4 |  2  2 | * 30  * |  1  3  0 |  3  3 0 | 3 1
. . x3o . . |  3 |  0  3 | *  * 30 |  0  2  2 |  1  4 1 | 2 2
------------+----+-------+---------+----------+---------+----
x3o x . . .   6 |  6  3 | 2  3  0 | 10  *  * |  3  0 0 | 3 0
x . x3o . .   6 |  3  6 | 0  3  2 |  * 30  * |  1  2 0 | 2 1
. . x3o3o .   4 |  0  6 | 0  0  4 |  *  * 15 |  0  2 1 | 1 2
------------+----+-------+---------+----------+---------+----
x3o x3o . .   9 |  9  9 | 3  9  3 |  3  3  0 | 10  * * | 2 0
x . x3o3o .   8 |  4 12 | 0  6  8 |  0  4  2 |  * 15 * | 1 1
. . x3o3o3o   5 |  0 10 | 0  0 10 |  0  0  5 |  *  * 3 | 0 2
------------+----+-------+---------+----------+---------+----
x3o x3o3o .  12 | 12 18 | 4 18 12 |  6 12  3 |  4  3 0 | 5 *
x . x3o3o3o  10 |  5 20 | 0 10 20 |  0 10 10 |  0  5 2 | * 3

ox xx3oo3oo3oo&#x   → height = sqrt(3)/2 = 0.866025
(pen || penp)

o. o.3o.3o.3o.    | 5  * |  4  2 0  0 |  6 1  8  0  0 | 4  4 12  0  0 | 1  6  8 0 0 | 4 2 0
.o .o3.o3.o3.o    | * 10 |  0  1 1  4 |  0 1  4  4  6 | 0  4  6  6  4 | 0  6  4 4 1 | 4 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x. .. .. ..    | 2  0 | 10  * *  * |  3 0  2  0  0 | 3  1  6  0  0 | 1  3  6 0 0 | 3 2 0
oo oo3oo3oo3oo&#x | 1  1 |  * 10 *  * |  0 1  4  0  0 | 0  4  6  0  0 | 0  6  4 0 0 | 4 1 0
.x .. .. .. ..    | 0  2 |  *  * 5  * |  0 1  0  4  0 | 0  4  0  6  0 | 0  6  0 4 0 | 4 0 1
.. .x .. .. ..    | 0  2 |  *  * * 20 |  0 0  1  1  3 | 0  1  3  3  3 | 0  3  3 3 1 | 3 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x.3o. .. ..    | 3  0 |  3  0 0  0 | 10 *  *  *  * | 2  0  2  0  0 | 1  1  4 0 0 | 2 2 0
ox .. .. .. ..&#x | 1  2 |  0  2 1  0 |  * 5  *  *  *  0  4  0  0  0 | 0  6  0 0 0 | 4 0 0
.. xx .. .. ..&#x | 2  2 |  1  2 0  1 |  * * 20  *  * | 0  1  3  0  0 | 0  3  3 0 0 | 3 1 0
.x .x .. .. ..    | 0  4 |  0  0 2  2 |  * *  * 10  * | 0  1  0  3  0 | 0  3  0 3 0 | 3 0 1
.. .x3.o .. ..    | 0  3 |  0  0 0  3 |  * *  *  * 20 | 0  0  1  1  2 | 0  1  2 2 1 | 2 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x.3o.3o. ..     4  0 |  6  0 0  0 |  4 0  0  0  0 | 5  *  *  *  * | 1  0  2 0 0 | 1 2 0
ox xx .. .. ..&#x  2  4 |  1  4 2  2 |  0 2  2  1  0 | * 10  *  *  * | 0  3  0 0 0 | 3 0 0
.. xx3oo .. ..&#x  3  3 |  3  3 0  3 |  1 0  3  0  1 | *  * 20  *  * | 0  1  2 0 0 | 2 1 0
.x .x3.o .. ..     0  6 |  0  0 3  6 |  0 0  0  3  2 | *  *  * 10  * | 0  1  0 2 0 | 2 0 1
.. .x3.o3.o ..     0  4 |  0  0 0  6 |  0 0  0  0  4 | *  *  *  * 10 | 0  0  1 1 1 | 1 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x.3o.3o.3o.     5  0 | 10  0 0  0 | 10 0  0  0  0 | 5  0  0  0  0 | 1  *  * * * | 0 2 0
ox xx3oo .. ..&#x  3  6 |  3  6 3  6 |  1 3  6  3  2 | 0  3  2  1  0 | * 10  * * * | 2 0 0
.. xx3oo3oo ..&#x  4  4 |  6  4 0  6 |  4 0  6  0  4 | 1  0  4  0  1 | *  * 10 * * | 1 1 0
.x .x3.o3.o ..     0  8 |  0  0 4 12 |  0 0  0  6  8 | 0  0  0  4  2 | *  *  * 5 * | 1 0 1
.. .x3.o3.o3.o     0  5 |  0  0 0 10 |  0 0  0  0 10 | 0  0  0  0  5 | *  *  * * 2 | 0 1 1
------------------+------+------------+---------------+---------------+-------------+------
ox xx3oo3oo ..&#x  4  8 |  6  8 4 12 |  4 4 12  6  8 | 1  6  8  4  2 | 0  4  2 1 0 | 5 * *
.. xx3oo3oo3oo&#x  5  5 | 10  5 0 10 | 10 0 10  0 10 | 5  0 10  0  5 | 1  0  5 0 1 | * 2 *
.x .x3.o3.o3.o     0 10 |  0  0 5 20 |  0 0  0 10 20 | 0  0  0 10 10 | 0  0  0 5 2 | * * 1

xx3oo ox3oo3oo&#x   → height = sqrt(5/8) = 0.790569
({3} || tratet)

o.3o. o.3o.3o.    | 3  * | 2  4  0  0 | 1  8  6 0  0  0 | 4 12  4 0  0 0 | 6  8 1 0 0 | 4 2 0
.o3.o .o3.o3.o    | * 12 | 0  1  2  3 | 0  2  3 1  6  3 | 1  6  3 3  6 1 | 3  6 1 3 2 | 3 2 1
------------------+------+------------+-----------------+----------------+------------+------
x. .. .. .. ..    | 2  0 | 3  *  *  * | 1  4  0 0  0  0 | 4  6  0 0  0 0 | 6  4 0 0 0 | 4 1 0
oo3oo oo3oo3oo&#x | 1  1 | * 12  *  * | 0  2  3 0  0  0 | 1  6  3 0  0 0 | 3  6 1 0 0 | 3 2 0
.x .. .. .. ..    | 0  2 | *  * 12  * | 0  1  0 1  3  0 | 1  3  0 3  3 0 | 3  3 0 3 1 | 3 1 1
.. .. .x .. ..    | 0  2 | *  *  * 18 | 0  0  1 0  2  2 | 0  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
------------------+------+------------+-----------------+----------------+------------+------
x.3o. .. .. ..    | 3  0 | 3  0  0  0 | 1  *  * *  *  *  4  0  0 0  0 0 | 6  0 0 0 0 | 4 0 0
xx .. .. .. ..&#x | 2  2 | 1  2  1  0 | * 12  * *  *  * | 1  3  0 0  0 0 | 3  3 0 0 0 | 3 1 0
.. .. ox .. ..&#x | 1  2 | 0  2  0  1 | *  * 18 *  *  * | 0  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x3.o .. .. ..    | 0  3 | 0  0  3  0 | *  *  * 4  *  * | 1  0  0 3  0 0 | 3  0 0 3 0 | 3 0 1
.x .. .x .. ..    | 0  4 | 0  0  2  2 | *  *  * * 18  * | 0  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
.. .. .x3.o ..    | 0  3 | 0  0  0  3 | *  *  * *  * 12 | 0  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
------------------+------+------------+-----------------+----------------+------------+------
xx3oo .. .. ..&#x  3  3 | 3  3  3  0 | 1  3  0 1  0  0 | 4  *  * *  * * | 3  0 0 0 0 | 3 0 0
xx .. ox .. ..&#x  2  4 | 1  4  2  2 | 0  2  2 0  1  0 | * 18  * *  * * | 1  2 0 0 0 | 2 1 0
.. .. ox3oo ..&#x  1  3 | 0  3  0  3 | 0  0  3 0  0  1 | *  * 12 *  * * | 0  2 1 0 0 | 1 2 0
.x3.o .x .. ..     0  6 | 0  0  6  3 | 0  0  0 2  3  0 | *  *  * 6  * * | 1  0 0 2 0 | 2 0 1
.x .. .x3.o ..     0  6 | 0  0  3  6 | 0  0  0 0  3  2 | *  *  * * 12 * | 0  1 0 1 1 | 1 1 1
.. .. .x3.o3.o     0  4 | 0  0  0  6 | 0  0  0 0  0  4 | *  *  * *  * 3 | 0  0 1 0 2 | 0 2 1
------------------+------+------------+-----------------+----------------+------------+------
xx3oo ox .. ..&#x  3  6 | 3  6  6  3 | 1  6  3 2  3  0 | 2  3  0 1  0 0 | 6  * * * * | 2 0 0
xx .. ox3oo ..&#x  2  6 | 1  6  3  6 | 0  3  6 0  3  2 | 0  3  2 0  1 0 | * 12 * * * | 1 1 0
.. .. ox3oo3oo&#x  1  4 | 0  4  0  6 | 0  0  6 0  0  4 | 0  0  4 0  0 1 | *  * 3 * * | 0 2 0
.x3.o .x3.o  ..    0  9 | 0  0  9  9 | 0  0  0 3  9  3 | 0  0  0 3  3 0 | *  * * 4 * | 1 0 1
.x .. .x3.o3.o.    0  8 | 0  0  4 12 | 0  0  0 0  6  8 | 0  0  0 0  4 2 | *  * * * 3 | 0 1 1
------------------+------+------------+-----------------+----------------+------------+------
xx3oo ox3oo ..&#x  3  9 | 3  9  9  9 | 1  9  9 3  9  3 | 3  9  3 3  3 0 | 3  3 0 1 0 | 4 * *
xx .. ox3oo3oo&#x  2  8 | 1  8  4 12 | 0  4 12 0  6  8 | 0  6  8 0  4 2 | 0  4 2 0 1 | * 3 *
.x3.o .x3.o3.o.    0 12 | 0  0 12 18 | 0  0  0 4 18 12 | 0  0  0 6 12 3 | 0  0 0 4 3 | * * 1

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