Acronym penpasc Name pentachoron-prismatic scalene,pentachoron-prism-pyramid pyramid,line atop fully orthogonal pentachoron prism |,>,O device line pyramid pyramid pyramid prism pyramid pyramid = |>>>|>> Circumradius sqrt(7/8) = 0.935414 Confer general polytopal classes: segmentoexa   scalene

Incidence matrix according to Dynkin symbol

```xo ox ox3oo3oo3oo&#x   → height = 1/sqrt(10) = 0.316228
(line || perp penp)

o. o. o.3o.3o.3o.    | 2  * | 1 10 0  0 | 10  5 20  0  0 | 5 20 10 20  0  0 | 10 20 10 10 0 0 | 10 10  5 2 0 | 5 2 1
.o .o .o3.o3.o3.o    | * 10 | 0  2 1  4 |  1  2  8  4  6 | 1  4  8 12  6  4 |  4  6 12  8 4 1 |  6  4  8 2 1 | 4 1 2
---------------------+------+-----------+----------------+------------------+-----------------+--------------+------
x. .. .. .. .. ..    | 2  0 | 1  * *  * ♦ 10  0  0  0  0 | 5 20  0  0  0  0 | 10 20  0  0 0 0 | 10 10  0 0 0 | 5 2 0
oo oo oo3oo3oo3oo&#x | 1  1 | * 20 *  * |  1  1  4  0  0 | 1  4  4  6  0  0 |  4  6  6  4 0 0 |  6  4  4 1 0 | 4 1 1
.. .x .. .. .. ..    | 0  2 | *  * 5  * |  0  2  0  4  0 | 1  0  8  0  6  0 |  4  0 12  0 4 0 |  6  0  8 0 1 | 4 0 2
.. .. .x .. .. ..    | 0  2 | *  * * 20 |  0  0  2  1  3 | 0  1  2  6  3  3 |  1  3  6  6 3 1 |  3  3  6 2 1 | 3 1 2
---------------------+------+-----------+----------------+------------------+-----------------+--------------+------
xo .. .. .. .. ..&#x | 2  1 | 1  2 0  0 | 10  *  *  *  * | 1  4  0  0  0  0 |  4  6  0  0 0 0 |  6  4  0 0 0 | 4 1 0
.. ox .. .. .. ..&#x | 1  2 | 0  2 1  0 |  * 10  *  *  * | 1  0  4  0  0  0 |  4  0  6  0 0 0 |  6  0  4 0 0 | 4 0 1
.. .. ox .. .. ..&#x | 1  2 | 0  2 0  1 |  *  * 40  *  * | 0  1  1  3  0  0 |  1  3  3  3 0 0 |  3  3  3 1 0 | 3 1 1
.. .x .x .. .. ..    | 0  4 | 0  0 2  2 |  *  *  * 10  * | 0  0  2  0  3  0 |  1  0  6  0 3 0 |  3  0  6 0 1 | 3 0 2
.. .. .x3.o .. ..    | 0  3 | 0  0 0  3 |  *  *  *  * 20 | 0  0  0  2  1  2 |  0  1  2  4 2 1 |  1  2  4 2 1 | 2 1 2
---------------------+------+-----------+----------------+------------------+-----------------+--------------+------
xo ox .. .. .. ..&#x ♦ 2  2 | 1  4 1  0 |  2  2  0  0  0 | 5  *  *  *  *  * ♦  4  0  0  0 0 0 |  6  0  0 0 0 | 4 0 0
xo .. ox .. .. ..&#x ♦ 2  2 | 1  4 0  1 |  2  0  2  0  0 | * 20  *  *  *  * |  1  3  0  0 0 0 |  3  3  0 0 0 | 3 1 0
.. ox ox .. .. ..&#x ♦ 1  4 | 0  4 2  2 |  0  2  2  1  0 | *  * 20  *  *  * |  1  0  3  0 0 0 |  3  0  3 0 0 | 3 0 1
.. .. ox3oo .. ..&#x ♦ 1  3 | 0  3 0  3 |  0  0  3  0  1 | *  *  * 40  *  * |  0  1  1  2 0 0 |  1  2  2 1 0 | 2 1 1
.. .x .x3.o .. ..    ♦ 0  6 | 0  0 3  6 |  0  0  0  3  2 | *  *  *  * 10  * |  0  0  2  0 2 0 |  1  0  4 0 1 | 2 0 2
.. .. .x3.o3.o ..    ♦ 0  4 | 0  0 0  6 |  0  0  0  0  4 | *  *  *  *  * 10 |  0  0  0  2 1 1 |  0  1  2 2 1 | 1 1 2
---------------------+------+-----------+----------------+------------------+-----------------+--------------+------
xo ox ox .. .. ..&#x ♦ 2  4 | 1  8 2  2 |  4  4  4  1  0 | 2  2  2  0  0  0 | 10  *  *  * * * |  3  0  0 0 0 | 3 0 0
xo .. ox3oo .. ..&#x ♦ 2  3 | 1  6 0  3 |  3  0  6  0  1 | 0  3  0  2  0  0 |  * 20  *  * * * |  1  2  0 0 0 | 2 1 0
.. ox ox3oo .. ..&#x ♦ 1  6 | 0  6 3  6 |  0  3  6  3  2 | 0  0  3  2  1  0 |  *  * 20  * * * |  1  0  2 0 0 | 2 0 1
.. .. ox3oo3oo ..&#x ♦ 1  4 | 0  4 0  6 |  0  0  6  0  4 | 0  0  0  4  0  1 |  *  *  * 20 * * |  0  1  1 1 0 | 1 1 1
.. .x .x3.o3.o ..    ♦ 0  8 | 0  0 4 12 |  0  0  0  6  8 | 0  0  0  0  4  2 |  *  *  *  * 5 * |  0  0  2 0 1 | 1 0 2
.. .. .x3.o3.o3.o    ♦ 0  5 | 0  0 0 10 |  0  0  0  0 10 | 0  0  0  0  0  5 |  *  *  *  * * 2 |  0  0  0 2 1 | 0 1 2
---------------------+------+-----------+----------------+------------------+-----------------+--------------+------
xo ox ox3oo .. ..&#x ♦ 2  6 | 1 12 3  6 |  6  6 12  3  2 | 3  6  6  4  1  0 |  3  2  2  0 0 0 | 10  *  * * * | 2 0 0
xo .. ox3oo3oo ..&#x ♦ 2  4 | 1  8 0  6 |  4  0 12  0  4 | 0  6  0  8  0  1 |  0  4  0  2 0 0 |  * 10  * * * | 1 1 0
.. ox ox3oo3oo ..&#x ♦ 1  8 | 0  8 4 12 |  0  4 12  6  8 | 0  0  6  8  4  2 |  0  0  4  2 1 0 |  *  * 10 * * | 1 0 1
.. .. ox3oo3oo3oo&#x ♦ 1  5 | 0  5 0 10 |  0  0 10  0 10 | 0  0  0 10  0  5 |  0  0  0  5 0 1 |  *  *  * 4 * | 0 1 1
.. .x .x3.o3.o3.o    ♦ 0 10 | 0  0 5 20 |  0  0  0 10 20 | 0  0  0  0 10 10 |  0  0  0  0 5 2 |  *  *  * * 1 | 0 0 2
---------------------+------+-----------+----------------+------------------+-----------------+--------------+------
xo ox ox3oo3oo ..&#x ♦ 2  8 | 1 16 4 12 |  8  8 24  6  8 | 4 12 12 16  4  2 |  6  8  8  4 1 0 |  4  2  2 0 0 | 5 * *
xo .. ox3oo3oo3oo&#x ♦ 2  5 | 1 10 0 10 |  5  0 20  0 10 | 0 10  0 20  0  5 |  0 10  0 10 0 1 |  0  5  0 2 0 | * 2 *
.. ox ox3oo3oo3oo&#x ♦ 1 10 | 0 10 5 20 |  0  5 20 10 20 | 0  0 10 20 10 10 |  0  0 10 10 5 2 |  0  0  5 2 1 | * * 2
```

```xoo oxx3ooo3ooo3ooo&#x   → height(1,2) = height(1,3) = sqrt(7/20) = 0.591608
height(2,3) = 1

o.. o..3o..3o..3o..    | 2 * * | 1  5  5  0 0  0 | 5 10  5 5 10  0  0  0 | 10 10 5 10 10 10 0  0 0 | 10  5 10 10 10  5 0 0 0 | 5 1 10  5 5 1 0 | 1 5 1 1
.o. .o.3.o.3.o.3.o.    | * 5 * | 0  2  0  4 1  0 | 1  8  2 0  0  6  4  0 |  4 12 1  8  0  0 4  6 0 |  6  8  4 12  0  0 1 4 0 | 4 2  6  8 0 0 1 | 1 4 2 0
..o ..o3..o3..o3..o    | * * 5 | 0  0  2  0 1  4 | 0  0  2 1  8  0  4  6 |  0  0 1  8  4 12 0  6 4 |  0  0  4 12  6  8 0 4 1 | 0 0  6  8 4 2 1 | 0 4 2 1
-----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+--------
x.. ... ... ... ...    | 2 0 0 | 1  *  *  * *  * ♦ 5  0  0 5  0  0  0  0 | 10  0 5  0 10  0 0  0 0 | 10  0 10  0 10  0 0 0 0 | 5 0 10  0 5 0 0 | 1 5 0 1
oo. oo.3oo.3oo.3oo.&#x | 1 1 0 | * 10  *  * *  * | 1  4  1 0  0  0  0  0 |  4  6 1  4  0  0 0  0 0 |  6  4  4  6  0  0 0 0 0 | 4 1  6  4 0 0 0 | 1 4 1 0
o.o o.o3o.o3o.o3o.o&#x | 1 0 1 | *  * 10  * *  * | 0  0  1 1  4  0  0  0 |  0  0 1  4  4  6 0  0 0 |  0  0  4  6  6  4 0 0 0 | 0 0  6  4 4 1 0 | 0 4 1 1
... .x. ... ... ...    | 0 2 0 | *  *  * 10 *  * | 0  2  0 0  0  3  1  0 |  1  6 0  2  0  0 3  3 0 |  3  6  1  6  0  0 1 3 0 | 3 2  3  6 0 0 1 | 1 3 2 0
.oo .oo3.oo3.oo3.oo&#x | 0 1 1 | *  *  *  * 5  * | 0  0  2 0  0  0  4  0 |  0  0 1  8  0  0 0  6 0 |  0  0  4 12  0  0 0 4 0 | 0 0  6  8 0 0 1 | 0 4 2 0
... ..x ... ... ...    | 0 0 2 | *  *  *  * * 10 | 0  0  0 0  2  0  1  3 |  0  0 0  2  1  6 0  3 3 |  0  0  1  6  3  6 0 3 1 | 0 0  3  6 3 2 1 | 0 3 2 1
-----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+--------
xo. ... ... ... ...&#x | 2 1 0 | 1  2  0  0 0  0 | 5  *  * *  *  *  *  * |  4  0 1  0  0  0 0  0 0 |  6  0  4  0  0  0 0 0 0 | 4 0  6  0 0 0 0 | 1 4 0 0
... ox. ... ... ...&#x | 1 2 0 | 0  2  0  1 0  0 | * 20  * *  *  *  *  * |  1  3 0  1  0  0 0  0 0 |  3  3  1  3  0  0 0 0 0 | 3 1  3  3 0 0 0 | 1 3 1 0
ooo ooo3ooo3ooo3ooo&#x | 1 1 1 | 0  1  1  0 1  0 | *  * 10 *  *  *  *  * |  0  0 1  4  0  0 0  0 0 |  0  0  4  6  0  0 0 0 0 | 0 0  6  4 0 0 0 | 0 4 1 0
x.o ... ... ... ...&#x | 2 0 1 | 1  0  2  0 0  0 | *  *  * 5  *  *  *  * |  0  0 1  0  4  0 0  0 0 |  0  0  4  0  6  0 0 0 0 | 0 0  6  0 4 0 0 | 0 4 0 1
... o.x ... ... ...&#x | 1 0 2 | 0  0  2  0 0  1 | *  *  * * 20  *  *  * |  0  0 0  1  1  3 0  0 0 |  0  0  1  3  3  3 0 0 0 | 0 0  3  3 3 1 0 | 0 3 1 1
... .x.3.o. ... ...    | 0 3 0 | 0  0  0  3 0  0 | *  *  * *  * 10  *  * |  0  2 0  0  0  0 2  1 0 |  1  4  0  2  0  0 1 2 0 | 2 2  1  4 0 0 1 | 1 2 2 0
... .xx ... ... ...&#x | 0 2 2 | 0  0  0  1 2  1 | *  *  * *  *  * 10  * |  0  0 0  2  0  0 0  3 0 |  0  0  1  6  0  0 0 3 0 | 0 0  3  6 0 0 1 | 0 3 1 0
... ..x3..o ... ...    | 0 0 3 | 0  0  0  0 0  3 | *  *  * *  *  *  * 10 |  0  0 0  0  0  2 0  1 2 |  0  0  0  2  1  4 0 2 1 | 0 0  1  4 2 2 1 | 0 2 2 1
-----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+--------
xo. ox. ... ... ...&#x ♦ 2 2 0 | 1  4  0  1 0  0 | 2  2  0 0  0  0  0  0 | 10  * *  *  *  * *  * * |  3  0  1  0  0  0 0 0 0 | 3 0  3  0 0 0 0 | 1 3 0 0
... ox.3oo. ... ...&#x ♦ 1 3 0 | 0  3  0  3 0  0 | 0  3  0 0  0  1  0  0 |  * 20 *  *  *  * *  * * |  1  2  0  1  0  0 0 0 0 | 2 1  1  2 0 0 0 | 1 2 1 0
xoo ... ... ... ...&#x ♦ 2 1 1 | 1  2  2  0 1  0 | 1  0  2 1  0  0  0  0 |  *  * 5  *  *  * *  * * ♦  0  0  4  0  0  0 0 0 0 | 0 0  6  0 0 0 0 | 0 4 0 0
... oxx ... ... ...&#x ♦ 1 2 2 | 0  2  2  1 2  1 | 0  1  2 0  1  0  1  0 |  *  * * 20  *  * *  * * |  0  0  1  3  0  0 0 0 0 | 0 0  3  3 0 0 0 | 0 3 1 0
x.o o.x ... ... ...&#x ♦ 2 0 2 | 1  0  4  0 0  1 | 0  0  0 2  2  0  0  0 |  *  * *  * 10  * *  * * |  0  0  1  0  3  0 0 0 0 | 0 0  3  0 3 0 0 | 0 3 0 1
... o.x3o.o ... ...&#x ♦ 1 0 3 | 0  0  3  0 0  3 | 0  0  0 0  3  0  0  1 |  *  * *  *  * 20 *  * * |  0  0  0  1  1  2 0 0 0 | 0 0  1  2 2 1 0 | 0 2 1 1
... .x.3.o.3.o. ...    ♦ 0 4 0 | 0  0  0  6 0  0 | 0  0  0 0  0  4  0  0 |  *  * *  *  *  * 5  * * |  0  2  0  0  0  0 1 1 0 | 1 2  0  2 0 0 1 | 1 1 2 0
... .xx3.oo ... ...&#x ♦ 0 3 3 | 0  0  0  3 3  3 | 0  0  0 0  0  1  3  1 |  *  * *  *  *  * * 10 * |  0  0  0  2  0  0 0 2 0 | 0 0  1  4 0 0 1 | 0 2 2 0
... ..x3..o3..o ...    ♦ 0 0 4 | 0  0  0  0 0  6 | 0  0  0 0  0  0  0  4 |  *  * *  *  *  * *  * 5 |  0  0  0  0  0  2 0 1 1 | 0 0  0  2 1 2 1 | 0 1 2 1
-----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+--------
xo. ox.3oo. ... ...&#x ♦ 2 3 0 | 1  6  0  3 0  0 | 3  6  0 0  0  1  0  0 |  3  2 0  0  0  0 0  0 0 | 10  *  *  *  *  * * * * | 2 0  1  0 0 0 0 | 1 2 0 0
... ox.3oo.3oo. ...&#x ♦ 1 4 0 | 0  4  0  6 0  0 | 0  6  0 0  0  4  0  0 |  0  4 0  0  0  0 1  0 0 |  * 10  *  *  *  * * * * | 1 1  0  1 0 0 0 | 1 1 1 0
xoo oxx ... ... ...&#x ♦ 2 2 2 | 1  4  4  1 2  1 | 2  2  4 2  2  0  1  0 |  1  0 2  2  1  0 0  0 0 |  *  * 10  *  *  * * * * | 0 0  3  0 0 0 0 | 0 3 0 0
... oxx3ooo ... ...&#x ♦ 1 3 3 | 0  3  3  3 3  3 | 0  3  3 0  3  1  3  1 |  0  1 0  3  0  1 0  1 0 |  *  *  * 20  *  * * * * | 0 0  1  2 0 0 0 | 0 2 1 0
x.o o.x3o.o ... ...&#x ♦ 2 0 3 | 1  0  6  0 0  3 | 0  0  0 3  6  0  0  1 |  0  0 0  0  3  2 0  0 0 |  *  *  *  * 10  * * * * | 0 0  1  0 2 0 0 | 0 2 0 1
... o.x3o.o3o.o ...&#x ♦ 1 0 4 | 0  0  4  0 0  6 | 0  0  0 0  6  0  0  4 |  0  0 0  0  0  4 0  0 1 |  *  *  *  *  * 10 * * * | 0 0  0  1 1 1 0 | 0 1 1 1
... .x.3.o.3.o.3.o.    ♦ 0 5 0 | 0  0  0 10 0  0 | 0  0  0 0  0 10  0  0 |  0  0 0  0  0  0 5  0 0 |  *  *  *  *  *  * 1 * * | 0 2  0  0 0 0 1 | 1 0 2 0
... .xx3.oo3.oo ...&#x ♦ 0 4 4 | 0  0  0  6 4  6 | 0  0  0 0  0  4  6  4 |  0  0 0  0  0  0 1  4 1 |  *  *  *  *  *  * * 5 * | 0 0  0  2 0 0 1 | 0 1 2 0
... ..x3..o3..o3..o    ♦ 0 0 5 | 0  0  0  0 0 10 | 0  0  0 0  0  0  0 10 |  0  0 0  0  0  0 0  0 5 |  *  *  *  *  *  * * * 1 | 0 0  0  0 0 2 1 | 0 0 2 1
-----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+--------
xo. ox.3oo.3oo. ...&#x ♦ 2 4 0 | 1  8  0  6 0  0 | 4 12  0 0  0  4  0  0 |  6  8 0  0  0  0 1  0 0 |  4  2  0  0  0  0 0 0 0 | 5 *  *  * * * * | 1 1 0 0
... ox.3oo.3oo.3oo.&#x ♦ 1 5 0 | 0  5  0 10 0  0 | 0 10  0 0  0 10  0  0 |  0 10 0  0  0  0 5  0 0 |  0  5  0  0  0  0 1 0 0 | * 2  *  * * * * | 1 0 1 0
xoo oxx3ooo ... ...&#x ♦ 2 3 3 | 1  6  6  3 3  3 | 3  6  6 3  6  1  3  1 |  3  2 3  6  3  2 0  1 0 |  1  0  3  2  1  0 0 0 0 | * * 10  * * * * | 0 2 0 0
... oxx3ooo3ooo ...&#x ♦ 1 4 4 | 0  4  4  6 4  6 | 0  6  4 0  6  4  6  4 |  0  4 0  6  0  4 1  4 1 |  0  1  0  4  0  1 0 1 0 | * *  * 10 * * * | 0 1 1 0
x.o o.x3o.o3o.o ...&#x ♦ 2 0 4 | 1  0  8  0 0  6 | 0  0  0 4 12  0  0  4 |  0  0 0  0  6  8 0  0 1 |  0  0  0  0  4  2 0 0 0 | * *  *  * 5 * * | 0 1 0 1
... o.x3o.o3o.o3o.o&#x ♦ 1 0 5 | 0  0  5  0 0 10 | 0  0  0 0 10  0  0 10 |  0  0 0  0  0 10 0  0 5 |  0  0  0  0  0  5 0 0 1 | * *  *  * * 2 * | 0 0 1 1
... .xx3.oo3.oo3.oo&#x ♦ 0 5 5 | 0  0  0 10 5 10 | 0  0  0 0  0 10 10 10 |  0  0 0  0  0  0 5 10 5 |  0  0  0  0  0  0 1 5 1 | * *  *  * * * 1 | 0 0 2 0
-----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+--------
xo. ox.3oo.3oo.3oo.&#x ♦ 2 5 0 | 1 10  0 10 0  0 | 5 20  0 0  0 10  0  0 | 10 20 0  0  0  0 5  0 0 | 10 10  0  0  0  0 1 0 0 | 5 2  0  0 0 0 0 | 1 * * *
xoo oxx3ooo3ooo ...&#x ♦ 2 4 4 | 1  8  8  6 4  6 | 4 12  8 4 12  4  6  4 |  6  8 4 12  6  8 1  4 1 |  4  2  6  8  4  2 0 1 0 | 1 0  4  2 1 0 0 | * 5 * *
... oxx3ooo3ooo3ooo&#x ♦ 1 5 5 | 0  5  5 10 5 10 | 0 10  5 0 10 10 10 10 |  0 10 0 10  0 10 5 10 5 |  0  5  0 10  0  5 1 5 1 | 0 1  0  5 0 1 1 | * * 2 *
x.o o.x3o.o3o.o3o.o&#x ♦ 2 0 5 | 1  0 10  0 0 10 | 0  0  0 5 20  0  0 10 |  0  0 0  0 10 20 0  0 5 |  0  0  0  0 10 10 0 0 1 | 0 0  0  0 5 2 0 | * * * 1
```