pendip

Acronym	pendip
Name	pentachoron duoprism, vertex figure of icoy
Circumradius	2/sqrt(5) = 0.894427
Inradius	1/sqrt(40) = 0.158114
Volume	5/9216 = 0.00054253
Surface	5 sqrt(10)/576 = 0.027450
Dihedral angles	at tetdip between tetpen and tetpen: 90° at trapen between tetpen and tetpen: arccos(1/4) = 75.522488°
Face vector	25, 100, 200, 250, 210, 120, 45, 10
Confer	general polytopal classes: Wythoffian polyzetta noble polytopes segmentozetta analogs: simplex duoprism S_n×S_n
External links

Incidence matrix according to Dynkin symbol

x3o3o3o x3o3o3o

. . . . . . . . | 25 |  4  4 |  6  16  6 |  4  24  24  4 | 1 16  36 16 1 |  4 24 24  4 |  6 16  6 | 4 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x . . . . . . . |  2 | 50  * |  3   4  0 |  3  12   6  0 | 1 12  18  4 0 |  4 18 12  1 |  6 12  3 | 4 3
. . . . x . . . |  2 |  * 50 |  0   4  3 |  0   6  12  3 | 0  4  18 12 1 |  1 12 18  4 |  3 12  6 | 3 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o . . . . . . |  3 |  3  0 | 50   *  * |  2   4   0  0 | 1  8   6  0 0 |  4 12  4  0 |  6  8  1 | 4 2
x . . . x . . . |  4 |  2  2 |  * 100  * |  0   3   3  0 | 0  3   9  3 0 |  1  9  9  1 |  3  9  3 | 3 3
. . . . x3o . . |  3 |  0  3 |  *   * 50 |  0   0   4  2 | 0  0   6  8 1 |  0  4 12  4 |  1  8  6 | 2 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o . . . . . ♦  4 |  6  0 |  4   0  0 | 25   *   *  * | 1  4   0  0 0 |  6  4  0  0 |  6  4  0 | 4 1
x3o . . x . . . ♦  6 |  6  3 |  2   3  0 |  * 100   *  * | 0  2   3  0 0 |  1  6  3  0 |  3  6  1 | 3 2
x . . . x3o . . ♦  6 |  3  6 |  0   3  2 |  *   * 100  * | 0  0   3  2 0 |  0  3  6  1 |  1  6  3 | 2 3
. . . . x3o3o . ♦  4 |  0  6 |  0   0  4 |  *   *   * 25 | 0  0   0  4 1 |  0  0  6  4 |  0  4  6 | 1 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o . . . . ♦  5 | 10  0 | 10   0  0 |  5   0   0  0 | 5  *   *  * * ♦  4  0  0  0 |  6  0  0 | 4 0
x3o3o . x . . . ♦  8 | 12  4 |  8   6  0 |  2   4   0  0 | * 50   *  * * |  1  3  0  0 |  3  3  0 | 3 1
x3o . . x3o . . ♦  9 |  9  9 |  3   9  3 |  0   3   3  0 | *  * 100  * * |  0  2  2  0 |  1  4  1 | 2 2
x . . . x3o3o . ♦  8 |  4 12 |  0   6  8 |  0   0   4  2 | *  *   * 50 * |  0  0  3  1 |  0  3  3 | 1 3
. . . . x3o3o3o ♦  5 |  0 10 |  0   0 10 |  0   0   0  5 | *  *   *  * 5 |  0  0  0  4 |  0  0  6 | 0 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o x . . . ♦ 10 | 20  5 | 20  10  0 | 10  10   0  0 | 2  5   0  0 0 | 10  *  *  * |  3  0  0 | 3 0
x3o3o . x3o . . ♦ 12 | 18 12 | 12  18  4 |  3  12   6  0 | 0  3   4  0 0 |  * 50  *  * |  1  2  0 | 2 1
x3o . . x3o3o . ♦ 12 | 12 18 |  4  18 12 |  0   6  12  3 | 0  0   4  3 0 |  *  * 50  * |  0  2  1 | 1 2
x . . . x3o3o3o ♦ 10 |  5 20 |  0  10 20 |  0   0  10 10 | 0  0   0  5 2 |  *  *  * 10 |  0  0  3 | 0 3
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o x3o . . ♦ 15 | 30 15 | 30  30  5 | 15  30  10  0 | 3 15  10  0 0 |  3  5  0  0 | 10  *  * | 2 0
x3o3o . x3o3o . ♦ 16 | 24 24 | 16  36 16 |  4  24  24  4 | 0  6  16  6 0 |  0  4  4  0 |  * 25  * | 1 1
x3o . . x3o3o3o ♦ 15 | 15 30 |  5  30 30 |  0  10  30 15 | 0  0  10 15 3 |  0  0  5  3 |  *  * 10 | 0 2
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o x3o3o . ♦ 20 | 40 30 | 40  60 20 | 20  60  40  5 | 4 30  40 10 0 |  6 20 10  0 |  4  5  0 | 5 *
x3o3o . x3o3o3o ♦ 20 | 30 40 | 20  60 40 |  5  40  60 20 | 0 10  40 30 4 |  0 10 20  6 |  0  5  4 | * 5

or
. . . . . . . .    | 25 |   8 |  12  16 |  8  48 |  2  32  36 |  8  48 | 12 16 |  8
-------------------+----+-----+---------+--------+------------+--------+-------+---
x . . . . . . .  & |  2 | 100 |   3   4 |  3  18 |  1  16  18 |  5  30 |  9 12 |  7
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o . . . . . .  & |  3 |   3 | 100   * |  2   4 |  1   8   6 |  4  16 |  7  8 |  6
x . . . x . . .    |  4 |   4 |   * 100 |  0   6 |  0   6   9 |  2  18 |  6  9 |  6
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o . . . . .  & ♦  4 |   6 |   4   0 | 50   * |  1   4   0 |  4   6 |  6  4 |  5
x3o . . x . . .  & ♦  6 |   9 |   2   3 |  * 200 |  0   2   3 |  1   9 |  4  6 |  5
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o . . . .  & ♦  5 |  10 |  10   0 |  5   0 | 10   *   * ♦  4   0 |  6  0 |  4
x3o3o . x . . .  & ♦  8 |  16 |   8   6 |  2   4 |  * 100   * |  1   3 |  3  3 |  4
x3o . . x3o . .    ♦  9 |  18 |   6   9 |  0   6 |  *   * 100 |  0   4 |  2  4 |  4
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o x . . .  & ♦ 10 |  25 |  20  10 | 10  10 |  2   5   0 | 20   * |  3  0 |  3
x3o3o . x3o . .  & ♦ 12 |  30 |  16  18 |  3  18 |  0   3   4 |  * 100 |  1  2 |  3
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o x3o . .  & ♦ 15 |  45 |  35  30 | 15  40 |  3  15  10 |  3   5 | 20  * |  2
x3o3o . x3o3o .    ♦ 16 |  48 |  32  36 |  8  48 |  0  12  16 |  0   8 |  * 25 |  2
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o x3o3o .  & ♦ 20 |  70 |  60  60 | 25 100 |  4  40  40 |  6  30 |  4  5 | 10

xx3oo3oo3oo ox3oo3oo&#x   height = sqrt(5/8) = 0.790569
(pen || tetpen)

o.3o.3o.3o. o.3o.3o.    | 5  * |  4  4  0  0 |  6 16  6  0  0  0 | 4 24 24  4  0  0  0 0 | 1 16 36 16 1 0  0  0  0 | 4 24 24  4 0  0  0 | 6 16  6 0 0 | 4 4 0
.o3.o3.o3.o .o3.o3.o    | * 20 |  0  1  4  3 |  0  4  3  6 12  3 | 0  6 12  3  4 18 12 1 | 0  4 18 12 1 1 12 18  4 | 1 12 18  4 3 12  6 | 3 12  6 3 4 | 3 4 1
------------------------+------+-------------+-------------------+-----------------------+-------------------------+--------------------+-------------+------
x. .. .. .. .. .. ..    | 2  0 | 10  *  *  * |  3  4  0  0  0  0 | 3 12  6  0  0  0  0 0 | 1 12 18  4 0 0  0  0  0 | 4 18 12  1 0  0  0 | 6 12  3 0 0 | 4 3 0
oo3oo3oo3oo oo3oo3oo&#x | 1  1 |  * 20  *  * |  0  4  3  0  0  0 | 0  6 12  3  0  0  0 0 | 0  4 18 12 1 0  0  0  0 | 1 12 18  4 0  0  0 | 3 12  6 0 0 | 3 4 0
.x .. .. .. .. .. ..    | 0  2 |  *  * 40  * |  0  1  0  3  3  0 | 0  3  3  0  3  9  3 0 | 0  3  9  3 0 1  9  9  1 | 1  9  9  1 3  9  3 | 3  9  3 3 3 | 3 3 1
.. .. .. .. .x .. ..    | 0  2 |  *  *  * 30 |  0  0  1  0  4  2 | 0  0  4  2  0  6  8 1 | 0  0  6  8 1 0  4 12  4 | 0  4 12  4 1  8  6 | 1  8  6 2 4 | 2 4 1
------------------------+------+-------------+-------------------+-----------------------+-------------------------+--------------------+-------------+------
x.3o. .. .. .. .. ..    | 3  0 |  3  0  0  0 | 10  *  *  *  *  * | 2  4  0  0  0  0  0 0 | 1  8  6  0 0 0  0  0  0 | 4 12  4  0 0  0  0 | 6  8  1 0 0 | 4 2 0
xx .. .. .. .. .. ..&#x | 2  2 |  1  2  1  0 |  * 40  *  *  *  * | 0  3  3  0  0  0  0 0 | 0  3  9  3 0 0  0  0  0 | 1  9  9  1 0  0  0 | 3  9  3 0 0 | 3 3 0
.. .. .. .. ox .. ..&#x | 1  2 |  0  2  0  1 |  *  * 30  *  *  * | 0  0  4  2  0  0  0 0 | 0  0  6  8 1 0  0  0  0 | 0  4 12  4 0  0  0 | 1  8  6 0 0 | 2 4 0
.x3.o .. .. .. .. ..    | 0  3 |  0  0  3  0 |  *  *  * 40  *  * | 0  1  0  0  2  3  0 0 | 0  2  3  0 0 1  6  3  0 | 1  6  3  0 3  6  1 | 3  6  1 3 2 | 3 2 1
.x .. .. .. .x .. ..    | 0  4 |  0  0  2  2 |  *  *  *  * 60  * | 0  0  1  0  0  3  2 0 | 0  0  3  2 0 0  3  6  1 | 0  3  6  1 1  6  3 | 1  6  3 2 3 | 2 3 1
.. .. .. .. .x3.o ..    | 0  3 |  0  0  0  3 |  *  *  *  *  * 20 | 0  0  0  1  0  0  4 1 | 0  0  0  4 1 0  0  6  4 | 0  0  6  4 0  4  6 | 0  4  6 1 4 | 1 4 1
------------------------+------+-------------+-------------------+-----------------------+-------------------------+--------------------+-------------+------
x.3o.3o. .. .. .. ..    ♦ 4  0 |  6  0  0  0 |  4  0  0  0  0  0 | 5  *  *  *  *  *  * * | 1  4  0  0 0 0  0  0  0 | 4  6  0  0 0  0  0 | 6  4  0 0 0 | 4 1 0
xx3oo .. .. .. .. ..&#x ♦ 3  3 |  3  3  3  0 |  1  3  0  1  0  0 | * 40  *  *  *  *  * * | 0  2  3  0 0 0  0  0  0 | 1  6  3  0 0  0  0 | 3  6  1 0 0 | 3 2 0
xx .. .. .. ox .. ..&#x ♦ 2  4 |  1  4  2  2 |  0  2  2  0  1  0 | *  * 60  *  *  *  * * | 0  0  3  2 0 0  0  0  0 | 0  3  6  1 0  0  0 | 1  6  3 0 0 | 2 3 0
.. .. .. .. ox3oo ..&#x ♦ 1  3 |  0  3  0  3 |  0  0  3  0  0  1 | *  *  * 20  *  *  * * | 0  0  0  4 1 0  0  0  0 | 0  0  6  4 0  0  0 | 0  4  6 0 0 | 1 4 0
.x3.o3.o .. .. .. ..    ♦ 0  4 |  0  0  6  0 |  0  0  0  4  0  0 | *  *  *  * 20  *  * * | 0  1  0  0 0 1  3  0  0 | 1  3  0  0 3  3  0 | 3  3  0 3 1 | 3 1 1
.x3.o .. .. .x .. ..    ♦ 0  6 |  0  0  6  3 |  0  0  0  2  3  0 | *  *  *  *  * 60  * * | 0  0  1  0 0 0  2  2  0 | 0  2  2  0 1  4  1 | 1  4  1 2 2 | 2 2 1
.x .. .. .. .x3.o ..    ♦ 0  6 |  0  0  3  6 |  0  0  0  0  3  2 | *  *  *  *  *  * 40 * | 0  0  0  1 0 0  0  3  1 | 0  0  3  1 0  3  3 | 0  3  3 1 3 | 1 3 1
.. .. .. .. .x3.o3.o    ♦ 0  4 |  0  0  0  6 |  0  0  0  0  0  4 | *  *  *  *  *  *  * 5 | 0  0  0  0 1 0  0  0  4 | 0  0  0  4 0  0  6 | 0  0  6 0 4 | 0 4 1
------------------------+------+-------------+-------------------+-----------------------+-------------------------+--------------------+-------------+------
x.3o.3o.3o. .. .. ..    ♦ 5  0 | 10  0  0  0 | 10  0  0  0  0  0 | 5  0  0  0  0  0  0 0 | 1  *  *  * * *  *  *  * ♦ 4  0  0  0 0  0  0 | 6  0  0 0 0 | 4 0 0
xx3oo3oo .. .. .. ..&#x ♦ 4  4 |  6  4  6  0 |  4  6  0  4  0  0 | 1  4  0  0  1  0  0 0 | * 20  *  * * *  *  *  * | 1  3  0  0 0  0  0 | 3  3  0 0 0 | 3 1 0
xx3oo .. .. ox .. ..&#x ♦ 3  6 |  3  6  6  3 |  1  6  3  2  3  0 | 0  2  3  0  0  1  0 0 | *  * 60  * * *  *  *  * | 0  2  2  0 0  0  0 | 1  4  1 0 0 | 2 2 0
xx .. .. .. ox3oo ..&#x ♦ 2  6 |  1  6  3  6 |  0  3  6  0  3  2 | 0  0  3  2  0  0  1 0 | *  *  * 40 * *  *  *  * | 0  0  3  1 0  0  0 | 0  3  3 0 0 | 1 3 0
.. .. .. .. ox3oo3oo&#x ♦ 1  4 |  0  4  0  6 |  0  0  6  0  0  4 | 0  0  0  4  0  0  0 1 | *  *  *  * 5 *  *  *  * ♦ 0  0  0  4 0  0  0 | 0  0  6 0 0 | 0 4 0
.x3.o3.o3.o .. .. ..    ♦ 0  5 |  0  0 10  0 |  0  0  0 10  0  0 | 0  0  0  0  5  0  0 0 | *  *  *  * * 4  *  *  * ♦ 1  0  0  0 3  0  0 | 3  0  0 3 0 | 3 0 1
.x3.o3.o .. .x .. ..    ♦ 0  8 |  0  0 12  4 |  0  0  0  8  6  0 | 0  0  0  0  2  4  0 0 | *  *  *  * * * 30  *  * | 0  1  0  0 1  2  0 | 1  2  0 2 1 | 2 1 1
.x3.o .. .. .x3.o ..    ♦ 0  9 |  0  0  9  9 |  0  0  0  3  9  3 | 0  0  0  0  0  3  3 0 | *  *  *  * * *  * 40  * | 0  0  1  0 0  2  1 | 0  2  1 1 2 | 1 2 1
.x .. .. .. .x3.o3.o    ♦ 0  8 |  0  0  4 12 |  0  0  0  0  6  8 | 0  0  0  0  0  0  4 2 | *  *  *  * * *  *  * 10 | 0  0  0  1 0  0  3 | 0  0  3 0 3 | 0 3 1
------------------------+------+-------------+-------------------+-----------------------+-------------------------+--------------------+-------------+------
xx3oo3oo3oo .. .. ..&#x ♦ 5  5 | 10  5 10  0 | 10 10  0 10  0  0 | 5 10  0  0  5  0  0 0 | 1  5  0  0 0 1  0  0  0 | 4  *  *  * *  *  * | 3  0  0 0 0 | 3 0 0
xx3oo3oo .. ox .. ..&#x ♦ 4  8 |  6  8 12  4 |  4 12  4  8  6  0 | 1  8  6  0  2  4  0 0 | 0  2  4  0 0 0  1  0  0 | * 30  *  * *  *  * | 1  2  0 0 0 | 2 1 0
xx3oo .. .. ox3oo ..&#x ♦ 3  9 |  3  9  9  9 |  1  9  9  3  9  3 | 0  3  9  3  0  3  3 0 | 0  0  3  3 0 0  0  1  0 | *  * 40  * *  *  * | 0  2  1 0 0 | 1 2 0
xx .. .. .. ox3oo3oo&#x ♦ 2  8 |  1  8  4 12 |  0  4 12  0  6  8 | 0  0  6  8  0  0  4 2 | 0  0  0  4 2 0  0  0  1 | *  *  * 10 *  *  * | 0  0  3 0 0 | 0 3 0
.x3.o3.o3.o .x .. ..    ♦ 0 10 |  0  0 20  5 |  0  0  0 20 10  0 | 0  0  0  0 10 10  0 0 | 0  0  0  0 0 2  5  0  0 | *  *  *  * 6  *  * | 1  0  0 2 0 | 2 0 1
.x3.o3.o .. .x3.o ..    ♦ 0 12 |  0  0 18 12 |  0  0  0 12 18  4 | 0  0  0  0  3 12  6 0 | 0  0  0  0 0 0  3  4  0 | *  *  *  * * 20  * | 0  1  0 1 1 | 1 1 1
.x3.o .. .. .x3.o3.o    ♦ 0 12 |  0  0 12 18 |  0  0  0  4 18 12 | 0  0  0  0  0  6 12 3 | 0  0  0  0 0 0  0  4  3 | *  *  *  * *  * 10 | 0  0  1 0 2 | 0 2 1
------------------------+------+-------------+-------------------+-----------------------+-------------------------+--------------------+-------------+------
xx3oo3oo3oo ox .. ..&#x ♦ 5 10 | 10 10 20  5 | 10 20  5 20 10  0 | 5 20 10  0 10 10  0 0 | 1 10 10  0 0 2  5  0  0 | 2  5  0  0 1  0  0 | 6  *  * * * | 2 0 0
xx3oo3oo .. ox3oo ..&#x ♦ 4 12 |  6 12 18 12 |  4 18 12 12 18  4 | 1 12 18  4  3 12  6 0 | 0  3 12  6 0 0  3  4  0 | 0  3  4  0 0  1  0 | * 20  * * * | 1 1 0
xx3oo .. .. ox3oo3oo&#x ♦ 3 12 |  3 12 12 18 |  1 12 18  4 18 12 | 0  4 18 12  0  6 12 3 | 0  0  6 12 3 0  0  4  3 | 0  0  4  3 0  0  1 | *  * 10 * * | 0 2 0
.x3.o3.o3.o .x3.o ..    ♦ 0 15 |  0  0 30 15 |  0  0  0 30 30  5 | 0  0  0  0 15 30 10 0 | 0  0  0  0 0 3 15 10  0 | 0  0  0  0 3  5  0 | *  *  * 4 * | 1 0 1
.x3.o3.o .. .x3.o3.o    ♦ 0 16 |  0  0 24 24 |  0  0  0 16 36 16 | 0  0  0  0  4 24 24 4 | 0  0  0  0 0 0  6 16  6 | 0  0  0  0 0  4  4 | *  *  * * 5 | 0 1 1
------------------------+------+-------------+-------------------+-----------------------+-------------------------+--------------------+-------------+------
xx3oo3oo3oo ox3oo ..&#x ♦ 5 15 | 10 15 30 15 | 10 30 15 30 30  5 | 5 30 30  5 15 30 10 0 | 1 15 30 10 0 3 15 10  0 | 3 15 10  0 3  5  0 | 3  5  0 1 0 | 4 * *
xx3oo3oo .. ox3oo3oo&#x ♦ 4 16 |  6 16 24 24 |  4 24 24 16 36 16 | 1 16 36 16  4 24 24 4 | 0  4 24 24 4 0  6 16  6 | 0  6 16  6 0  4  4 | 0  4  4 0 1 | * 5 *
.x3.o3.o3.o .x3.o3.o    ♦ 0 20 |  0  0 40 30 |  0  0  0 40 60 20 | 0  0  0  0 20 60 40 5 | 0  0  0  0 0 4 30 40 10 | 0  0  0  0 6 20 10 | 0  0  0 4 5 | * * 1

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