Acronym trarap Name triangle - rectified-pentachoron duoprism,vertex figure of branq Circumradius sqrt(14/15) = 0.966092 Volume 11 sqrt(15)/384 = 0.110945 Confer more general: n,rap-dip   general polytopal classes: segmentopeta

Incidence matrix according to Dynkin symbol

```x3o o3x3o3o

. . . . . . | 30 |  2  6 |  1 12  3  6 |  6  6 12  3  2 |  3  6  6  4 1 | 3 2 2
------------+----+-------+-------------+----------------+---------------+------
x . . . . . |  2 | 30  * |  1  6  0  0 |  6  3  6  0  0 |  3  6  3  2 0 | 3 2 1
. . . x . . |  2 |  * 90 |  0  2  1  2 |  1  2  4  2  1 |  1  2  4  2 1 | 2 1 2
------------+----+-------+-------------+----------------+---------------+------
x3o . . . . |  3 |  3  0 | 10  *  *  * ♦  6  0  0  0  0 |  3  6  0  0 0 | 3 2 0
x . . x . . |  4 |  2  2 |  * 90  *  * |  1  1  2  0  0 |  1  2  2  1 0 | 2 1 1
. . o3x . . |  3 |  0  3 |  *  * 30  * |  0  2  0  2  0 |  1  0  4  0 1 | 2 0 2
. . . x3o . |  3 |  0  3 |  *  *  * 60 |  0  0  2  1  1 |  0  1  2  2 1 | 1 1 2
------------+----+-------+-------------+----------------+---------------+------
x3o . x . . ♦  6 |  6  3 |  2  3  0  0 | 30  *  *  *  * |  1  2  0  0 0 | 2 1 0
x . o3x . . ♦  6 |  3  6 |  0  3  2  0 |  * 30  *  *  * |  1  0  2  0 0 | 2 0 1
x . . x3o . ♦  6 |  3  6 |  0  3  0  2 |  *  * 60  *  * |  0  1  1  1 0 | 1 1 1
. . o3x3o . ♦  6 |  0 12 |  0  0  4  4 |  *  *  * 15  * |  0  0  2  0 1 | 1 0 2
. . . x3o3o ♦  4 |  0  6 |  0  0  0  4 |  *  *  *  * 15 |  0  0  0  2 1 | 0 1 2
------------+----+-------+-------------+----------------+---------------+------
x3o o3x . . ♦  9 |  9  9 |  3  9  3  0 |  3  3  0  0  0 | 10  *  *  * * | 2 0 0
x3o . x3o . ♦  9 |  9  9 |  3  9  0  3 |  3  0  3  0  0 |  * 20  *  * * | 1 1 0
x . o3x3o . ♦ 12 |  6 24 |  0 12  8  8 |  0  4  4  2  0 |  *  * 15  * * | 1 0 1
x . . x3o3o ♦  8 |  4 12 |  0  6  0  8 |  0  0  4  0  2 |  *  *  * 15 * | 0 1 1
. . o3x3o3o ♦ 10 |  0 30 |  0  0 10 20 |  0  0  0  5  5 |  *  *  *  * 3 | 0 0 2
------------+----+-------+-------------+----------------+---------------+------
x3o o3x3o . ♦ 18 | 18 36 |  6 36 12 12 | 12 12 12  3  0 |  4  4  3  0 0 | 5 * *
x3o . x3o3o ♦ 12 | 12 18 |  4 18  0 12 |  6  0 12  0  3 |  0  4  0  3 0 | * 5 *
x . o3x3o3o ♦ 20 | 10 60 |  0 30 20 40 |  0 10 20 10 10 |  0  0  5  5 2 | * * 3
```

```ox oo3xx3oo3oo&#x   → height = sqrt(3)/2 = 0.866025
(rap || rappip)

o. o.3o.3o.3o.    | 10  * |  6  2  0  0 |  3  6  1 12  0  0  0 | 3 2  6  6 12  0  0  0  0 | 1  3  6  6  4 0 0 0 | 3 2 2 0
.o .o3.o3.o3.o    |  * 20 |  0  1  1  6 |  0  0  1  6  6  3  6 | 0 0  6  3  6  3  6  3  2 | 0  3  6  3  2 3 2 1 | 3 2 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. .. x. .. ..    |  2  0 | 30  *  *  * |  1  2  0  2  0  0  0 | 2 1  1  2  4  0  0  0  0 | 1  1  2  4  2 0 0 0 | 2 1 2 0
oo oo3oo3oo3oo&#x |  1  1 |  * 20  *  * |  0  0  1  6  0  0  0 | 0 0  6  3  6  0  0  0  0 | 0  3  6  3  2 0 0 0 | 3 2 1 0
.x .. .. .. ..    |  0  2 |  *  * 10  * |  0  0  1  0  6  0  0 | 0 0  6  0  0  3  6  0  0 | 0  3  6  0  0 3 2 0 | 3 2 0 1
.. .. .x .. ..    |  0  2 |  *  *  * 60 |  0  0  0  1  1  1  2 | 0 0  1  1  2  1  2  2  1 | 0  1  2  2  1 2 1 1 | 2 1 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. o.3x. .. ..    |  3  0 |  3  0  0  0 | 10  *  *  *  *  *  * | 2 0  0  2  0  0  0  0  0 | 1  1  0  4  0 0 0 0 | 2 0 2 0
.. .. x.3o. ..    |  3  0 |  3  0  0  0 |  * 20  *  *  *  *  * | 1 1  0  0  2  0  0  0  0 | 1  0  1  2  2 0 0 0 | 1 1 2 0
ox .. .. .. ..&#x |  1  2 |  0  2  1  0 |  *  * 10  *  *  *  * ♦ 0 0  6  0  0  0  0  0  0 | 0  3  6  0  0 0 0 0 | 3 2 0 0
.. .. xx .. ..&#x |  2  2 |  1  2  0  1 |  *  *  * 60  *  *  * | 0 0  1  1  2  0  0  0  0 | 0  1  2  2  1 0 0 0 | 2 1 1 0
.x .. .x .. ..    |  0  4 |  0  0  2  2 |  *  *  *  * 30  *  * | 0 0  1  0  0  1  2  0  0 | 0  1  2  0  0 2 1 0 | 2 1 0 1
.. .o3.x .. ..    |  0  3 |  0  0  0  3 |  *  *  *  *  * 20  * | 0 0  0  1  0  1  0  2  0 | 0  1  0  2  0 2 0 1 | 2 0 1 1
.. .. .x3.o ..    |  0  3 |  0  0  0  3 |  *  *  *  *  *  * 40 | 0 0  0  0  1  0  1  1  1 | 0  0  1  1  1 1 1 1 | 1 1 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. o.3x.3o. ..    ♦  6  0 | 12  0  0  0 |  4  4  0  0  0  0  0 | 5 *  *  *  *  *  *  *  * | 1  0  0  2  0 0 0 0 | 1 0 2 0
.. .. x.3o.3o.    ♦  4  0 |  6  0  0  0 |  0  4  0  0  0  0  0 | * 5  *  *  *  *  *  *  * | 1  0  0  0  2 0 0 0 | 0 1 2 0
ox .. xx .. ..&#x ♦  2  4 |  1  4  2  2 |  0  0  2  2  1  0  0 | * * 30  *  *  *  *  *  * | 0  1  2  0  0 0 0 0 | 2 1 0 0
.. oo3xx .. ..&#x ♦  3  3 |  3  3  0  3 |  1  0  0  3  0  1  0 | * *  * 20  *  *  *  *  * | 0  1  0  2  0 0 0 0 | 2 0 1 0
.. .. xx3oo ..&#x ♦  3  3 |  3  3  0  3 |  0  1  0  3  0  0  1 | * *  *  * 40  *  *  *  * | 0  0  1  1  1 0 0 0 | 1 1 1 0
.x .o3.x .. ..    ♦  0  6 |  0  0  3  6 |  0  0  0  0  3  2  0 | * *  *  *  * 10  *  *  * | 0  1  0  0  0 2 0 0 | 2 0 0 1
.x .. .x3.o ..    ♦  0  6 |  0  0  3  6 |  0  0  0  0  3  0  2 | * *  *  *  *  * 20  *  * | 0  0  1  0  0 1 1 0 | 1 1 0 1
.. .o3.x3.o ..    ♦  0  6 |  0  0  0 12 |  0  0  0  0  0  4  4 | * *  *  *  *  *  * 10  * | 0  0  0  1  0 1 0 1 | 1 0 1 1
.. .. .x3.o3.o    ♦  0  4 |  0  0  0  6 |  0  0  0  0  0  0  4 | * *  *  *  *  *  *  * 10 | 0  0  0  0  1 0 1 1 | 0 1 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. o.3x.3o.3o.    ♦ 10  0 | 30  0  0  0 | 10 20  0  0  0  0  0 | 5 5  0  0  0  0  0  0  0 | 1  *  *  *  * * * * | 0 0 2 0
ox oo3xx .. ..&#x ♦  3  6 |  3  6  3  6 |  1  0  3  6  3  2  0 | 0 0  3  2  0  1  0  0  0 | * 10  *  *  * * * * | 2 0 0 0
ox .. xx3oo ..&#x ♦  3  6 |  3  6  3  6 |  0  1  3  6  3  0  2 | 0 0  3  0  2  0  1  0  0 | *  * 20  *  * * * * | 1 1 0 0
.. oo3xx3oo ..&#x ♦  6  6 | 12  6  0 12 |  4  4  0 12  0  4  4 | 1 0  0  4  4  0  0  1  0 | *  *  * 10  * * * * | 1 0 1 0
.. .. xx3oo3oo&#x ♦  4  4 |  6  4  0  6 |  0  4  0  6  0  0  4 | 0 1  0  0  4  0  0  0  1 | *  *  *  * 10 * * * | 0 1 1 0
.x .o3.x3.o ..    ♦  0 12 |  0  0  6 24 |  0  0  0  0 12  8  8 | 0 0  0  0  0  4  4  2  0 | *  *  *  *  * 5 * * | 1 0 0 1
.x .. .x3.o3.o    ♦  0  8 |  0  0  4 12 |  0  0  0  0  6  0  8 | 0 0  0  0  0  0  4  0  2 | *  *  *  *  * * 5 * | 0 1 0 1
.. .o3.x3.o3.o    ♦  0 10 |  0  0  0 30 |  0  0  0  0  0 10 20 | 0 0  0  0  0  0  0  5  5 | *  *  *  *  * * * 2 | 0 0 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
ox oo3xx3oo ..&#x ♦  6 12 | 12 12  6 24 |  4  4  6 24 12  8  8 | 1 0 12  8  8  4  4  2  0 | 0  4  4  2  0 1 0 0 | 5 * * *
ox .. xx3oo3oo&#x ♦  4  8 |  6  8  4 12 |  0  4  4 12  6  0  8 | 0 1  6  0  8  0  4  0  2 | 0  0  4  0  2 0 1 0 | * 5 * *
.. oo3xx3oo3oo&#x ♦ 10 10 | 30 10  0 30 | 10 20  0 30  0 10 20 | 5 5  0 10 20  0  0  5  5 | 1  0  0  5  5 0 0 1 | * * 2 *
.x .o3.x3.o3.o    ♦  0 20 |  0  0 10 60 |  0  0  0  0 30 20 40 | 0 0  0  0  0 10 20 10 10 | 0  0  0  0  0 5 5 2 | * * * 1
```

```xx3oo xo3ox3oo&#x   → height = sqrt(5/8) = 0.790569
(tratet || troct)

o.3o. o.3o.3o.    | 12  * |  2  3  3  0  0 | 1  6  3  6  3  3 0  0  0  0 | 3  6 1  3  6  6  3  1  0  0  0 0 | 3 2 3  3  6  2 1 0 0 0 | 1 3 1 2 0
.o3.o .o3.o3.o    |  * 18 |  0  0  2  2  4 | 0  0  0  4  1  4 1  8  2  2 | 0  0 0  2  2  8  2  2  4  4  4 1 | 0 0 1  4  4  4 1 2 2 2 | 0 2 2 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x. .. .. .. ..    |  2  0 | 12  *  *  *  * | 1  3  0  3  0  0 0  0  0  0 | 3  3 0  3  3  3  0  0  0  0  0 0 | 3 1 3  3  3  1 0 0 0 0 | 1 3 1 1 0
.. .. x. .. ..    |  2  0 |  * 18  *  *  * | 0  2  2  0  1  0 0  0  0  0 | 1  4 1  0  2  0  2  0  0  0  0 0 | 2 2 1  0  4  0 1 0 0 0 | 1 2 0 2 0
oo3oo oo3oo3oo&#x |  1  1 |  *  * 36  *  * | 0  0  0  2  1  2 0  0  0  0 | 0  0 0  1  2  4  2  1  0  0  0 0 | 0 0 1  2  4  2 1 0 0 0 | 0 2 1 2 0
.x .. .. .. ..    |  0  2 |  *  *  * 18  * | 0  0  0  2  0  0 1  4  0  0 | 0  0 0  2  1  4  0  0  4  2  2 0 | 0 0 1  4  2  2 0 2 2 1 | 0 2 2 1 1
.. .. .. .x ..    |  0  2 |  *  *  *  * 36 | 0  0  0  0  0  1 0  2  1  1 | 0  0 0  0  0  2  1  1  1  2  2 1 | 0 0 0  1  2  2 1 1 1 2 | 0 1 1 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. .. .. ..    |  3  0 |  3  0  0  0  0 | 4  *  *  *  *  * *  *  *  * ♦ 3  0 0  3  0  0  0  0  0  0  0 0 | 3 0 3  3  0  0 0 0 0 0 | 1 3 1 0 0
x. .. x. .. ..    |  4  0 |  2  2  0  0  0 | * 18  *  *  *  * *  *  *  * | 1  2 0  0  1  0  0  0  0  0  0 0 | 2 1 1  0  2  0 0 0 0 0 | 1 2 0 1 0
.. .. x.3o. ..    |  3  0 |  0  3  0  0  0 | *  * 12  *  *  * *  *  *  * | 0  2 1  0  0  0  1  0  0  0  0 0 | 1 2 0  0  2  0 1 0 0 0 | 1 1 0 2 0
xx .. .. .. ..&#x |  2  2 |  1  0  2  1  0 | *  *  * 36  *  * *  *  *  * | 0  0 0  1  1  2  0  0  0  0  0 0 | 0 0 1  2  2  1 0 0 0 0 | 0 2 1 1 0
.. .. xo .. ..&#x |  2  1 |  0  1  2  0  0 | *  *  *  * 18  * *  *  *  * | 0  0 0  0  2  0  2  0  0  0  0 0 | 0 0 1  0  4  0 1 0 0 0 | 0 2 0 2 0
.. .. .. ox ..&#x |  1  2 |  0  0  2  0  1 | *  *  *  *  * 36 *  *  *  * | 0  0 0  0  0  2  1  1  0  0  0 0 | 0 0 0  1  2  2 1 0 0 0 | 0 1 1 2 0
.x3.o .. .. ..    |  0  3 |  0  0  0  3  0 | *  *  *  *  *  * 6  *  *  * ♦ 0  0 0  2  0  0  0  0  4  0  0 0 | 0 0 1  4  0  0 0 2 2 0 | 0 2 2 0 1
.x .. .. .x ..    |  0  4 |  0  0  0  2  2 | *  *  *  *  *  * * 36  *  * | 0  0 0  0  0  1  0  0  1  1  1 0 | 0 0 0  1  1  1 0 1 1 1 | 0 1 1 1 1
.. .. .o3.x ..    |  0  3 |  0  0  0  0  3 | *  *  *  *  *  * *  * 12  * | 0  0 0  0  0  0  1  0  0  2  0 1 | 0 0 0  0  2  0 1 1 0 2 | 0 1 0 2 1
.. .. .. .x3.o    |  0  3 |  0  0  0  0  3 | *  *  *  *  *  * *  *  * 12 | 0  0 0  0  0  0  0  1  0  0  2 1 | 0 0 0  0  0  2 1 0 1 2 | 0 0 1 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. x. .. ..    ♦  6  0 |  6  3  0  0  0 | 2  3  0  0  0  0 0  0  0  0 | 6  * *  *  *  *  *  *  *  *  * * | 2 0 1  0  0  0 0 0 0 0 | 1 2 0 0 0
x. .. x.3o. ..    ♦  6  0 |  3  6  0  0  0 | 0  3  2  0  0  0 0  0  0  0 | * 12 *  *  *  *  *  *  *  *  * * | 1 1 0  0  1  0 0 0 0 0 | 1 1 0 1 0
.. .. x.3o.3o.    ♦  4  0 |  0  6  0  0  0 | 0  0  4  0  0  0 0  0  0  0 | *  * 3  *  *  *  *  *  *  *  * * | 0 2 0  0  0  0 1 0 0 0 | 1 0 0 2 0
xx3oo .. .. ..&#x ♦  3  3 |  3  0  3  3  0 | 1  0  0  3  0  0 1  0  0  0 | *  * * 12  *  *  *  *  *  *  * * | 0 0 1  2  0  0 0 0 0 0 | 0 2 1 0 0
xx .. xo .. ..&#x ♦  4  2 |  2  2  4  1  0 | 0  1  0  2  2  0 0  0  0  0 | *  * *  * 18  *  *  *  *  *  * * | 0 0 1  0  2  0 0 0 0 0 | 0 2 0 1 0
xx .. .. ox ..&#x ♦  2  4 |  1  0  4  2  2 | 0  0  0  2  0  2 0  1  0  0 | *  * *  *  * 36  *  *  *  *  * * | 0 0 0  1  1  1 0 0 0 0 | 0 1 1 1 0
.. .. xo3ox ..&#x ♦  3  3 |  0  3  6  0  3 | 0  0  1  0  3  3 0  0  1  0 | *  * *  *  *  * 12  *  *  *  * * | 0 0 0  0  2  0 1 0 0 0 | 0 1 0 2 0
.. .. .. ox3oo&#x ♦  1  3 |  0  0  3  0  3 | 0  0  0  0  0  3 0  0  0  1 | *  * *  *  *  *  * 12  *  *  * * | 0 0 0  0  0  2 1 0 0 0 | 0 0 1 2 0
.x3.o .. .x ..    ♦  0  6 |  0  0  0  6  3 | 0  0  0  0  0  0 2  3  0  0 | *  * *  *  *  *  *  * 12  *  * * | 0 0 0  1  0  0 0 1 1 0 | 0 1 1 0 1
.x .. .o3.x ..    ♦  0  6 |  0  0  0  3  6 | 0  0  0  0  0  0 0  3  2  0 | *  * *  *  *  *  *  *  * 12  * * | 0 0 0  0  1  0 0 1 0 1 | 0 1 0 1 1
.x .. .. .x3.o    ♦  0  6 |  0  0  0  3  6 | 0  0  0  0  0  0 0  3  0  2 | *  * *  *  *  *  *  *  *  * 12 * | 0 0 0  0  0  1 0 0 1 1 | 0 0 1 1 1
.. .. .o3.x3.o    ♦  0  6 |  0  0  0  0 12 | 0  0  0  0  0  0 0  0  4  4 | *  * *  *  *  *  *  *  *  *  * 3 | 0 0 0  0  0  0 1 0 0 2 | 0 0 0 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. x.3o. ..    ♦  9  0 |  9  9  0  0  0 | 3  9  3  0  0  0 0  0  0  0 | 3  3 0  0  0  0  0  0  0  0  0 0 | 4 * *  *  *  * * * * * | 1 1 0 0 0
x. .. x.3o.3o.    ♦  8  0 |  4 12  0  0  0 | 0  6  8  0  0  0 0  0  0  0 | 0  4 2  0  0  0  0  0  0  0  0 0 | * 3 *  *  *  * * * * * | 1 0 0 1 0
xx3oo xo .. ..&#x ♦  6  3 |  6  3  6  3  0 | 2  3  0  6  3  0 1  0  0  0 | 1  0 0  2  3  0  0  0  0  0  0 0 | * * 6  *  *  * * * * * | 0 2 0 0 0
xx3oo .. ox ..&#x ♦  3  6 |  3  0  6  6  3 | 1  0  0  6  0  3 2  3  0  0 | 0  0 0  2  0  3  0  0  1  0  0 0 | * * * 12  *  * * * * * | 0 1 1 0 0
xx .. xo3ox ..&#x ♦  6  6 |  3  6 12  3  6 | 0  3  2  6  6  6 0  3  2  0 | 0  1 0  0  3  3  2  0  0  1  0 0 | * * *  * 12  * * * * * | 0 1 0 1 0
xx .. .. ox3oo&#x ♦  2  6 |  1  0  6  3  6 | 0  0  0  3  0  6 0  3  0  2 | 0  0 0  0  0  3  0  2  0  0  1 0 | * * *  *  * 12 * * * * | 0 0 1 1 0
.. .. xo3ox3oo&#x ♦  4  6 |  0  6 12  0 12 | 0  0  4  0  6 12 0  0  4  4 | 0  0 1  0  0  0  4  4  0  0  0 1 | * * *  *  *  * 3 * * * | 0 0 0 2 0
.x3.o .o3.x ..    ♦  0  9 |  0  0  0  9  9 | 0  0  0  0  0  0 3  9  3  0 | 0  0 0  0  0  0  0  0  3  3  0 0 | * * *  *  *  * * 4 * * | 0 1 0 0 1
.x3.o .. .x3.o    ♦  0  9 |  0  0  0  9  9 | 0  0  0  0  0  0 3  9  0  3 | 0  0 0  0  0  0  0  0  3  0  3 0 | * * *  *  *  * * * 4 * | 0 0 1 0 1
.x .. .o3.x3.o    ♦  0 12 |  0  0  0  6 24 | 0  0  0  0  0  0 0 12  8  8 | 0  0 0  0  0  0  0  0  0  4  4 2 | * * *  *  *  * * * * 3 | 0 0 0 1 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. x.3o.3o.    ♦ 12  0 | 12 18  0  0  0 | 4 18 12  0  0  0 0  0  0  0 | 6 12 3  0  0  0  0  0  0  0  0 0 | 4 3 0  0  0  0 0 0 0 0 | 1 * * * *
xx3oo xo3ox ..&#x ♦  9  9 |  9  9 18  9  9 | 3  9  3 18  9  9 3  9  3  0 | 3  3 0  6  9  9  3  0  3  3  0 0 | 1 0 3  3  3  0 0 1 0 0 | * 4 * * *
xx3oo .. ox3oo&#x ♦  3  9 |  3  0  9  9  9 | 1  0  0  9  0  9 3  9  0  3 | 0  0 0  3  0  9  0  3  3  0  3 0 | 0 0 0  3  0  3 0 0 1 0 | * * 4 * *
xx .. xo3ox3oo&#x ♦  8 12 |  4 12 24  6 24 | 0  6  8 12 12 24 0 12  8  8 | 0  4 2  0  6 12  8  8  0  4  4 2 | 0 1 0  0  4  4 2 0 0 1 | * * * 3 *
.x3.o .o3.x3.o    ♦  0 18 |  0  0  0 18 36 | 0  0  0  0  0  0 6 36 12 12 | 0  0 0  0  0  0  0  0 12 12 12 3 | 0 0 0  0  0  0 0 4 4 3 | * * * * 1
```