Acronym	squapen
Name	square-pentachoron duoprism, vertex figure of bersa
|,>,O device	line pyramid pyramid pyramid prism prism = |>>>||
Circumradius	sqrt(9/10) = 0.948683
Volume	sqrt(5)/96 = 0.023292
Dihedral angles	at pen between penp and penp:   90° at tepe between penp and squatet:   90° at tisdip between squatet and squatet:   arccos(1/4) = 75.522487°
Face vector	20, 60, 85, 70, 34, 9
Confer	more general: n,pen-dip   general polytopal classes: Wythoffian polypeta   segmentopeta   lace simplices
External links

Incidence matrix according to Dynkin symbol

x4o x3o3o3o

. . . . . . | 20 |  2  4 | 1  8  6 |  4 12  4 |  6  8 1 | 4 2
------------+----+-------+---------+----------+---------+----
x . . . . . |  2 | 20  * | 1  4  0 |  4  6  0 |  6  4 0 | 4 1
. . x . . . |  2 |  * 40 | 0  2  3 |  1  6  3 |  3  6 1 | 3 2
------------+----+-------+---------+----------+---------+----
x4o . . . . |  4 |  4  0 | 5  *  * ♦  4  0  0 |  6  0 0 | 4 0
x . x . . . |  4 |  2  2 | * 40  * |  1  3  0 |  3  3 0 | 3 1
. . x3o . . |  3 |  0  3 | *  * 40 |  0  2  2 |  1  4 1 | 2 2
------------+----+-------+---------+----------+---------+----
x4o x . . . ♦  8 |  8  4 | 2  4  0 | 10  *  * |  3  0 0 | 3 0
x . x3o . . ♦  6 |  3  6 | 0  3  2 |  * 40  * |  1  2 0 | 2 1
. . x3o3o . ♦  4 |  0  6 | 0  0  4 |  *  * 20 |  0  2 1 | 1 2
------------+----+-------+---------+----------+---------+----
x4o x3o . . ♦ 12 | 12 12 | 3 12  4 |  3  4  0 | 10  * * | 2 0
x . x3o3o . ♦  8 |  4 12 | 0  6  8 |  0  4  2 |  * 20 * | 1 1
. . x3o3o3o ♦  5 |  0 10 | 0  0 10 |  0  0  5 |  *  * 4 | 0 2
------------+----+-------+---------+----------+---------+----
x4o x3o3o . ♦ 16 | 16 24 | 4 24 16 |  6 16  4 |  4  4 0 | 5 *
x . x3o3o3o ♦ 10 |  5 20 | 0 10 20 |  0 10 10 |  0  5 2 | * 4

x x x3o3o3o

. . . . . . | 20 |  1  1  4 | 1  4  4  6 |  4  6  6  4 |  6  4  4 1 | 4 1 1
------------+----+----------+------------+-------------+------------+------
x . . . . . |  2 | 10  *  * | 1  4  0  0 |  4  6  0  0 |  6  4  0 0 | 4 1 0
. x . . . . |  2 |  * 10  * | 1  0  4  0 |  4  0  6  0 |  6  0  4 0 | 4 0 1
. . x . . . |  2 |  *  * 40 | 0  1  1  3 |  1  3  3  3 |  3  3  3 1 | 3 1 1
------------+----+----------+------------+-------------+------------+------
x x . . . . |  4 |  2  2  0 | 5  *  *  * ♦  4  0  0  0 |  6  0  0 0 | 4 0 0
x . x . . . |  4 |  2  0  2 | * 20  *  * |  1  3  0  0 |  3  3  0 0 | 3 1 0
. x x . . . |  4 |  0  2  2 | *  * 20  * |  1  0  3  0 |  3  0  3 0 | 3 0 1
. . x3o . . |  3 |  0  0  3 | *  *  * 40 |  0  1  1  2 |  1  2  2 1 | 2 1 1
------------+----+----------+------------+-------------+------------+------
x x x . . . ♦  8 |  4  4  4 | 2  2  2  0 | 10  *  *  * |  3  0  0 0 | 3 0 0
x . x3o . . ♦  6 |  3  0  6 | 0  3  0  2 |  * 20  *  * |  1  2  0 0 | 2 1 0
. x x3o . . ♦  6 |  0  3  6 | 0  0  3  2 |  *  * 20  * |  1  0  2 0 | 2 0 1
. . x3o3o . ♦  4 |  0  0  6 | 0  0  0  4 |  *  *  * 20 |  0  1  1 1 | 1 1 1
------------+----+----------+------------+-------------+------------+------
x x x3o . . ♦ 12 |  6  6 12 | 3  6  6  4 |  3  2  2  0 | 10  *  * * | 2 0 0
x . x3o3o . ♦  8 |  4  0 12 | 0  6  0  8 |  0  4  0  2 |  * 10  * * | 1 1 0
. x x3o3o . ♦  8 |  0  4 12 | 0  0  6  8 |  0  0  4  2 |  *  * 10 * | 1 0 1
. . x3o3o3o ♦  5 |  0  0 10 | 0  0  0 10 |  0  0  0  5 |  *  *  * 4 | 0 1 1
------------+----+----------+------------+-------------+------------+------
x x x3o3o . ♦ 16 |  8  8 24 | 4 12 12 16 |  6  8  8  4 |  4  2  2 0 | 5 * *
x . x3o3o3o ♦ 10 |  5  0 20 | 0 10  0 20 |  0 10  0 10 |  0  5  0 2 | * 2 *
. x x3o3o3o ♦ 10 |  0  5 20 | 0  0 10 20 |  0  0 10 10 |  0  0  5 2 | * * 2

xx xx3oo3oo3oo&#x   → height = 1
(penp || penp)

o. o.3o.3o.3o.    & | 20 |  1  4  1 |  4  6 1  4 |  6  4  4  6 |  4 1  6  4 | 1 4 1
--------------------+----+----------+------------+-------------+------------+------
x. .. .. .. ..    & |  2 | 10  *  * |  4  0 1  0 |  6  0  4  0 |  4 0  6  0 | 1 4 0
.. x. .. .. ..    & |  2 |  * 40  * |  1  3 0  1 |  3  3  1  3 |  3 1  3  3 | 1 3 1
oo oo3oo3oo3oo&#x   |  2 |  *  * 10 |  0  0 1  4 |  0  0  4  6 |  0 0  6  4 | 0 4 1
--------------------+----+----------+------------+-------------+------------+------
x. x. .. .. ..    & |  4 |  2  2  0 | 20  * *  * |  3  0  1  0 |  3 0  3  0 | 1 3 0
.. x.3o. .. ..    & |  3 |  0  3  0 |  * 40 *  * |  1  2  0  1 |  2 1  1  2 | 1 2 1
xx .. .. .. ..&#x   |  4 |  2  0  2 |  *  * 5  * ♦  0  0  4  0 |  0 0  6  0 | 0 4 0
.. xx .. .. ..&#x   |  4 |  0  2  2 |  *  * * 20 |  0  0  1  3 |  0 0  3  3 | 0 3 1
--------------------+----+----------+------------+-------------+------------+------
x. x.3o. .. ..    & ♦  6 |  3  6  0 |  3  2 0  0 | 20  *  *  * |  2 0  1  0 | 1 2 0
.. x.3o.3o. ..    & ♦  4 |  0  6  0 |  0  4 0  0 |  * 20  *  * |  1 1  0  1 | 1 1 1
xx xx .. .. ..&#x   ♦  8 |  4  4  4 |  2  0 2  2 |  *  * 10  * |  0 0  3  0 | 0 3 0
.. xx3oo .. ..&#x   ♦  6 |  0  6  3 |  0  2 0  3 |  *  *  * 20 |  0 0  1  2 | 0 2 1
--------------------+----+----------+------------+-------------+------------+------
x. x.3o.3o. ..    & ♦  8 |  4 12  0 |  6  8 0  0 |  4  2  0  0 | 10 *  *  * | 1 1 0
.. x.3o.3o.3o.    & ♦  5 |  0 10  0 |  0 10 0  0 |  0  5  0  0 |  * 4  *  * | 1 0 1
xx xx3oo .. ..&#x   ♦ 12 |  6 12  6 |  6  4 3  6 |  2  0  3  2 |  * * 10  * | 0 2 0
.. xx3oo3oo ..&#x   ♦  8 |  0 12  4 |  0  8 0  6 |  0  2  0  4 |  * *  * 10 | 0 1 1
--------------------+----+----------+------------+-------------+------------+------
x. x.3o.3o.3o.    & ♦ 10 |  5 20  0 | 10 20 0  0 | 10 10  0  0 |  5 2  0  0 | 2 * *
xx xx3oo3oo ..&#x   ♦ 16 |  8 24  8 | 12 16 4 12 |  8  4  6  8 |  2 0  4  2 | * 5 *
.. xx3oo3oo3oo&#x   ♦ 10 |  0 20  5 |  0 20 0 10 |  0 10  0 10 |  0 2  0  5 | * * 2

xx4oo ox3oo3oo&#x   → height = sqrt(5/8) = 0.790569
({4} || squatet)

o.4o. o.3o.3o.    | 4  * | 2  4  0  0 | 1  8  6 0  0  0 | 4 12  4 0  0 0 | 6  8 1 0 0 | 4 2 0
.o4.o .o3.o3.o    | * 16 | 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 | 4  *  *  * | 1  4  0 0  0  0 | 4  6  0 0  0 0 | 6  4 0 0 0 | 4 1 0
oo4oo oo3oo3oo&#x | 1  1 | * 16  *  * | 0  2  3 0  0  0 | 1  6  3 0  0 0 | 3  6 1 0 0 | 3 2 0
.x .. .. .. ..    | 0  2 | *  * 16  * | 0  1  0 1  3  0 | 1  3  0 3  3 0 | 3  3 0 3 1 | 3 1 1
.. .. .x .. ..    | 0  2 | *  *  * 24 | 0  0  1 0  2  2 | 0  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
------------------+------+------------+-----------------+----------------+------------+------
x.4o. .. .. ..    | 4  0 | 4  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 | * 16  * *  *  * | 1  3  0 0  0 0 | 3  3 0 0 0 | 3 1 0
.. .. ox .. ..&#x | 1  2 | 0  2  0  1 | *  * 24 *  *  * | 0  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x4.o .. .. ..    | 0  4 | 0  0  4  0 | *  *  * 4  *  * ♦ 1  0  0 3  0 0 | 3  0 0 3 0 | 3 0 1
.x .. .x .. ..    | 0  4 | 0  0  2  2 | *  *  * * 24  * | 0  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
.. .. .x3.o ..    | 0  3 | 0  0  0  3 | *  *  * *  * 16 | 0  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
------------------+------+------------+-----------------+----------------+------------+------
xx4oo .. .. ..&#x ♦ 4  4 | 4  4  4  0 | 1  4  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 | * 24  * *  * * | 1  2 0 0 0 | 1 2 0
.. .. ox3oo ..&#x ♦ 1  3 | 0  3  0  3 | 0  0  3 0  0  1 | *  * 16 *  * * | 0  2 1 0 0 | 1 2 0
.x4.o .x .. ..    ♦ 0  8 | 0  0  8  4 | 0  0  0 2  4  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 | *  *  * * 16 * | 0  1 0 1 1 | 1 1 1
.. .. .x3.o3.o    ♦ 0  4 | 0  0  0  6 | 0  0  0 0  0  4 | *  *  * *  * 4 | 0  0 1 0 2 | 0 2 1
------------------+------+------------+-----------------+----------------+------------+------
xx4oo ox .. ..&#x ♦ 4  8 | 4  8  8  4 | 1  8  4 2  4  0 | 2  4  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 | * 16 * * * | 1 1 0
.. .. ox3oo3oo&#x ♦ 1  4 | 0  4  0  6 | 0  0  6 0  0  4 | 0  0  4 0  0 1 | *  * 4 * * | 0 2 0
.x4.o .x3.o ..    ♦ 0 12 | 0  0 12 12 | 0  0  0 3 12  4 | 0  0  0 3  4 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 | *  * * * 4 | 0 1 1
------------------+------+------------+-----------------+----------------+------------+------
xx4oo ox3oo ..&#x ♦ 4 12 | 4 12 12 12 | 1 12 12 3 12  4 | 3 12  4 3  4 0 | 3  4 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 | * 4 *
.x4.o .x3.o3.o    ♦ 0 16 | 0  0 16 24 | 0  0  0 4 24 16 | 0  0  0 6 16 4 | 0  0 0 4 4 | * * 1