Acronym	petet
Name	pentagon-tetrahedron duoprism, pentagon duofastegium
	©
Circumradius	sqrt[(35+4 sqrt(5))/40] = 1.048144
Volume	sqrt[50+20 sqrt(5)]/48 = 0.202760
Face vector	20, 50, 54, 31, 9
Confer	more general: n,tet-dip   general polytopal classes: segmentotera
External links

Incidence matrix according to Dynkin symbol

x5o x3o3o

. . . . . | 20 |  2  3 | 1  6  3 | 3  6 1 | 3 2
----------+----+-------+---------+--------+----
x . . . . |  2 | 20  * | 1  3  0 | 3  3 0 | 3 1
. . x . . |  2 |  * 30 | 0  2  2 | 1  4 1 | 2 2
----------+----+-------+---------+--------+----
x5o . . . |  5 |  5  0 | 4  *  * | 3  0 0 | 3 0
x . x . . |  4 |  2  2 | * 30  * | 1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 20 | 0  2 1 | 1 2
----------+----+-------+---------+--------+----
x5o x . . ♦ 10 | 10  5 | 2  5  0 | 6  * * | 2 0
x . x3o . ♦  6 |  3  6 | 0  3  2 | * 20 * | 1 1
. . x3o3o ♦  4 |  0  6 | 0  0  4 | *  * 5 | 0 2
----------+----+-------+---------+--------+----
x5o x3o . ♦ 15 | 15 15 | 3 15  5 | 3  5 0 | 4 *
x . x3o3o ♦  8 |  4 12 | 0  6  8 | 0  4 2 | * 5

ox3oo xx5oo&#x   → height = sqrt(2/3) = 0.816497
({5} || trapedip)

o.3o. o.5o.    | 5  * | 2  3  0  0 | 1  3  6 0  0 0 | 1  6 3 0 0 | 2 3 0
.o3.o .o5.o    | * 15 | 0  1  2  2 | 0  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
---------------+------+------------+----------------+------------+------
.. .. x. ..    | 2  0 | 5  *  *  * | 1  0  3 0  0 0 | 0  3 3 0 0 | 1 3 0
oo3oo oo5oo&#x | 1  1 | * 15  *  * | 0  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x .. .. ..    | 0  2 | *  * 15  * | 0  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
.. .. .x ..    | 0  2 | *  *  * 15 | 0  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
---------------+------+------------+----------------+------------+------
.. .. x.5o.    | 5  0 | 5  0  0  0 | 1  *  * *  * * | 0  0 3 0 0 | 0 3 0
ox .. .. ..&#x | 1  2 | 0  2  1  0 | * 15  * *  * * | 1  2 0 0 0 | 2 1 0
.. .. xx ..&#x | 2  2 | 1  2  0  1 | *  * 15 *  * * | 0  2 1 0 0 | 1 2 0
.x3.o .. ..    | 0  3 | 0  0  3  0 | *  *  * 5  * * | 1  0 0 2 0 | 2 0 1
.x .. .x ..    | 0  4 | 0  0  2  2 | *  *  * * 15 * | 0  1 0 1 1 | 1 1 1
.. .. .x5.o    | 0  5 | 0  0  0  5 | *  *  * *  * 3 | 0  0 1 0 2 | 0 2 1
---------------+------+------------+----------------+------------+------
ox3oo .. ..&#x ♦ 1  3 | 0  3  3  0 | 0  3  0 1  0 0 | 5  * * * * | 2 0 0
ox .. xx ..&#x ♦ 2  4 | 1  4  2  2 | 0  2  2 0  1 0 | * 15 * * * | 1 1 0
.. .. xx5oo&#x ♦ 5  5 | 5  5  0  5 | 1  0  5 0  0 1 | *  * 3 * * | 0 2 0
.x3.o .x ..    ♦ 0  6 | 0  0  6  3 | 0  0  0 2  3 0 | *  * * 5 * | 1 0 1
.x .. .xn.o    ♦ 0 10 | 0  0  5 10 | 0  0  0 0  5 2 | *  * * * 3 | 0 1 1
---------------+------+------------+----------------+------------+------
ox3oo xx ..    ♦ 2  6 | 1  6  6  3 | 0  6  3 2  3 0 | 2  3 0 1 0 | 5 * *
ox .. xx5oo&#x ♦ 5 10 | 5 10  5 10 | 1  5 10 0  5 2 | 0  5 2 0 1 | * 3 *
.x3.o .x5.o    ♦ 0 15 | 0  0 15 15 | 0  0  0 5 15 3 | 0  0 0 5 3 | * * 1

ox xo xx5oo&#x   → height = 1/sqrt(2) = 0.707107
(pip || lacing-ortho pip)

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