Acronym decap Name decachoron prism Circumradius 1.5 Volume 115 sqrt(5)/48 = 5.357246 Confer general polytopal classes: segmentotera   lace simplices Externallinks

Incidence matrix according to Dynkin symbol

```x o3x3x3o

. . . . . | 60 |  1  2  2 |  2  2  1  4  1 |  1  4  1  2  2 | 2 2 1
----------+----+----------+----------------+----------------+------
x . . . . |  2 | 30  *  * |  2  2  0  0  0 |  1  4  1  0  0 | 2 2 0
. . x . . |  2 |  * 60  * |  1  0  1  2  0 |  1  2  0  2  1 | 2 1 1
. . . x . |  2 |  *  * 60 |  0  1  0  2  1 |  0  2  1  1  2 | 1 2 1
----------+----+----------+----------------+----------------+------
x . x . . |  4 |  2  2  0 | 30  *  *  *  * |  1  2  0  0  0 | 2 1 0
x . . x . |  4 |  2  0  2 |  * 30  *  *  * |  0  2  1  0  0 | 1 2 0
. o3x . . |  3 |  0  3  0 |  *  * 20  *  * |  1  0  0  2  0 | 2 0 1
. . x3x . |  6 |  0  3  3 |  *  *  * 40  * |  0  1  0  1  1 | 1 1 1
. . . x3o |  3 |  0  0  3 |  *  *  *  * 20 |  0  0  1  0  2 | 0 2 1
----------+----+----------+----------------+----------------+------
x o3x . . ♦  6 |  3  6  0 |  3  0  2  0  0 | 10  *  *  *  * | 2 0 0
x . x3x . ♦ 12 |  6  6  6 |  3  3  0  2  0 |  * 20  *  *  * | 1 1 0
x . . x3o ♦  6 |  3  0  6 |  0  3  0  0  2 |  *  * 10  *  * | 0 2 0
. o3x3x . ♦ 12 |  0 12  6 |  0  0  4  4  0 |  *  *  * 10  * | 1 0 1
. . x3x3o ♦ 12 |  0  6 12 |  0  0  0  4  4 |  *  *  *  * 10 | 0 1 1
----------+----+----------+----------------+----------------+------
x o3x3x . ♦ 24 | 12 24 12 | 12  6  8  8  0 |  4  4  0  2  0 | 5 * *
x . x3x3o ♦ 24 | 12 12 24 |  6 12  0  8  8 |  0  4  4  0  2 | * 5 *
. o3x3x3o ♦ 30 |  0 30 30 |  0  0 10 20 10 |  0  0  0  5  5 | * * 2
```
```or
. . . . .    | 60 |  1   4 |  4  2  4 |  2  4  4 |  4 1
-------------+----+--------+----------+----------+-----
x . . . .    |  2 | 30   * |  4  0  0 |  2  4  0 |  4 0
. . x . .  & |  2 |  * 120 |  1  1  2 |  1  2  3 |  3 1
-------------+----+--------+----------+----------+-----
x . x . .  & |  4 |  2   2 | 60  *  * |  1  2  0 |  3 0
. o3x . .  & |  3 |  0   3 |  * 40  * |  1  0  2 |  2 1
. . x3x .    |  6 |  0   6 |  *  * 40 |  0  1  2 |  2 1
-------------+----+--------+----------+----------+-----
x o3x . .  & ♦  6 |  3   6 |  3  2  0 | 20  *  * |  2 0
x . x3x .    ♦ 12 |  6  12 |  6  0  2 |  * 20  * |  2 0
. o3x3x .  & ♦ 12 |  0  18 |  0  4  4 |  *  * 20 |  1 1
-------------+----+--------+----------+----------+-----
x o3x3x .  & ♦ 24 | 12  36 | 18  8  8 |  4  4  2 | 10 *
. o3x3x3o    ♦ 30 |  0  60 |  0 20 20 |  0  0 10 |  * 2
```

```oo3xx3xx3oo&#x   → height = 1
(deca || deca)

o.3o.3o.3o.    | 30  * |  2  2  1  0  0 |  1  4  1  2  2  0  0  0 | 2 2  1  4  1 0 0 | 1 2 2 0
.o3.o3.o3.o    |  * 30 |  0  0  1  2  2 |  0  0  0  2  2  1  4  1 | 0 0  1  4  1 2 2 | 0 2 2 1
---------------+-------+----------------+-------------------------+------------------+--------
.. x. .. ..    |  2  0 | 30  *  *  *  * |  1  2  0  1  0  0  0  0 | 2 1  1  2  0 0 0 | 1 2 1 0
.. .. x. ..    |  2  0 |  * 30  *  *  * |  0  2  1  0  1  0  0  0 | 1 2  0  2  1 0 0 | 1 1 2 0
oo3oo3oo3oo&#x |  1  1 |  *  * 30  *  * |  0  0  0  2  2  0  0  0 | 0 0  1  4  1 0 0 | 0 2 2 0
.. .x .. ..    |  0  2 |  *  *  * 30  * |  0  0  0  1  0  1  2  0 | 0 0  1  2  0 2 1 | 0 2 1 1
.. .. .x ..    |  0  2 |  *  *  *  * 30 |  0  0  0  0  1  0  2  1 | 0 0  0  2  1 1 2 | 0 1 2 1
---------------+-------+----------------+-------------------------+------------------+--------
o.3x. .. ..    |  3  0 |  3  0  0  0  0 | 10  *  *  *  *  *  *  * | 2 0  1  0  0 0 0 | 1 2 0 0
.. x.3x. ..    |  6  0 |  3  3  0  0  0 |  * 20  *  *  *  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
.. .. x.3o.    |  3  0 |  0  3  0  0  0 |  *  * 10  *  *  *  *  * | 0 2  0  0  1 0 0 | 1 0 2 0
.. xx .. ..&#x |  2  2 |  1  0  2  1  0 |  *  *  * 30  *  *  *  * | 0 0  1  2  0 0 0 | 0 2 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 |  *  *  *  * 30  *  *  * | 0 0  0  2  1 0 0 | 0 1 2 0
.o3.x .. ..    |  0  3 |  0  0  0  3  0 |  *  *  *  *  * 10  *  * | 0 0  1  0  0 2 0 | 0 2 0 1
.. .x3.x ..    |  0  6 |  0  0  0  3  3 |  *  *  *  *  *  * 20  * | 0 0  0  1  0 1 1 | 0 1 1 1
.. .. .x3.o    |  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 10 | 0 0  0  0  1 0 2 | 0 0 2 1
---------------+-------+----------------+-------------------------+------------------+--------
o.3x.3x. ..    ♦ 12  0 | 12  6  0  0  0 |  4  4  0  0  0  0  0  0 | 5 *  *  *  * * * | 1 1 0 0
.. x.3x.3o.    ♦ 12  0 |  6 12  0  0  0 |  0  4  4  0  0  0  0  0 | * 5  *  *  * * * | 1 0 1 0
oo3xx .. ..&#x ♦  3  3 |  3  0  3  3  0 |  1  0  0  3  0  1  0  0 | * * 10  *  * * * | 0 2 0 0
.. xx3xx ..&#x ♦  6  6 |  3  3  6  3  3 |  0  1  0  3  3  0  1  0 | * *  * 20  * * * | 0 1 1 0
.. .. xx3oo&#x ♦  3  3 |  0  3  3  0  3 |  0  0  1  0  3  0  0  1 | * *  *  * 10 * * | 0 0 2 0
.o3.x3.x ..    ♦  0 12 |  0  0  0 12  6 |  0  0  0  0  0  4  4  0 | * *  *  *  * 5 * | 0 1 0 1
.. .x3.x3.o    ♦  0 12 |  0  0  0  6 12 |  0  0  0  0  0  0  4  4 | * *  *  *  * * 5 | 0 0 1 1
---------------+-------+----------------+-------------------------+------------------+--------
o.3x.3x.3o.    ♦ 30  0 | 30 30  0  0  0 | 10 20 10  0  0  0  0  0 | 5 5  0  0  0 0 0 | 1 * * *
oo3xx3xx ..&#x ♦ 12 12 | 12  6 12 12  6 |  4  4  0 12  6  4  4  0 | 1 0  4  4  0 1 0 | * 5 * *
.. xx3xx3oo&#x ♦ 12 12 |  6 12 12  6 12 |  0  4  4  6 12  0  4  4 | 0 1  0  4  4 0 1 | * * 5 *
.o3.x3.x3.o    ♦  0 30 |  0  0  0 30 30 |  0  0  0  0  0 10 20 10 | 0 0  0  0  0 5 5 | * * * 1
```
```or
o.3o.3o.3o.       | 30  * |  4  1  0 |  2  4  4  0  0 |  4  2  4  0 | 1  4 0
.o3.o3.o3.o       |  * 30 |  0  1  4 |  0  0  4  2  4 |  0  2  4  4 | 0  4 1
------------------+-------+----------+----------------+-------------+-------
.. x. .. ..     & |  2  0 | 60  *  * |  1  2  1  0  0 |  3  1  2  0 | 1  3 0
oo3oo3oo3oo&#x    |  1  1 |  * 30  * |  0  0  4  0  0 |  0  2  4  0 | 0  4 0
.. .x .. ..     & |  0  2 |  *  * 60 |  0  0  1  1  2 |  0  1  2  3 | 0  3 1
------------------+-------+----------+----------------+-------------+-------
o.3x. .. ..     & |  3  0 |  3  0  0 | 20  *  *  *  * |  2  1  0  0 | 1  2 0
.. x.3x. ..       |  6  0 |  6  0  0 |  * 20  *  *  * |  2  0  1  0 | 1  2 0
.. xx .. ..&#x  & |  2  2 |  1  2  1 |  *  * 60  *  * |  0  1  2  0 | 0  3 0
.o3.x .. ..     & |  0  3 |  0  0  3 |  *  *  * 20  * |  0  1  0  2 | 0  2 1
.. .x3.x ..       |  0  6 |  0  0  6 |  *  *  *  * 20 |  0  0  1  2 | 0  2 1
------------------+-------+----------+----------------+-------------+-------
o.3x.3x. ..     & ♦ 12  0 | 18  0  0 |  4  4  0  0  0 | 10  *  *  * | 1  1 0
oo3xx .. ..&#x  & ♦  3  3 |  3  3  3 |  1  0  3  1  0 |  * 20  *  * | 0  2 0
.. xx3xx ..&#x    ♦  6  6 |  6  6  6 |  0  1  6  0  1 |  *  * 20  * | 0  2 0
.o3.x3.x ..     & ♦  0 12 |  0  0 18 |  0  0  0  4  4 |  *  *  * 10 | 0  1 1
------------------+-------+----------+----------------+-------------+-------
o.3x.3x.3o.       ♦ 30  0 | 60  0  0 | 20 20  0  0  0 | 10  0  0  0 | 1  * *
oo3xx3xx ..&#x  & ♦ 12 12 | 18 12 18 |  4  4 18  4  4 |  1  4  4  1 | * 10 *
.o3.x3.x3.o       ♦  0 30 |  0  0 60 |  0  0  0 20 20 |  0  0  0 10 | *  * 1
```