Acronym	roc
Name	rectified octaexon
Circumradius	sqrt(3)/2 = 0.866025
External links

Incidence matrix according to Dynkin symbol

o3x3o3o3o3o3o

. . . . . . . | 28 ♦  12 |  6  30 | 15  40 | 20  30 | 15 12 | 6 2
--------------+----+-----+--------+--------+--------+-------+----
. x . . . . . |  2 | 168 |  1   5 |  5  10 | 10  10 | 10  5 | 5 1
--------------+----+-----+--------+--------+--------+-------+----
o3x . . . . . |  3 |   3 | 56   * ♦  5   0 | 10   0 | 10  0 | 5 0
. x3o . . . . |  3 |   3 |  * 280 |  1   4 |  4   6 |  6  4 | 4 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o . . . . ♦  6 |  12 |  4   4 | 70   * ♦  4   0 |  6  0 | 4 0
. x3o3o . . . ♦  4 |   6 |  0   4 |  * 280 |  1   3 |  3  3 | 3 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o . . . ♦ 10 |  30 | 10  20 |  5   5 | 56   * |  3  0 | 3 0
. x3o3o3o . . ♦  5 |  10 |  0  10 |  0   5 |  * 168 |  1  2 | 2 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o3o . . ♦ 15 |  60 | 20  60 | 15  30 |  6   6 | 28  * | 2 0
. x3o3o3o3o . ♦  6 |  15 |  0  20 |  0  15 |  0   6 |  * 56 | 1 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o3o3o . ♦ 21 | 105 | 35 140 | 35 105 | 21  42 |  7  7 | 8 *
. x3o3o3o3o3o ♦  7 |  21 |  0  35 |  0  35 |  0  21 |  0  7 | * 8

xo3ox3oo3oo3oo3oo&#x   → height = 2/sqrt(7) = 0.755929
(hop || ril)

o.3o.3o.3o.3o.3o.    | 7  * ♦  6  6   0 | 15  6  15  0   0 | 20 15  20  0   0 | 15 20  15  0  0 | 6 15  6 0 0 | 1 6 1 0
.o3.o3.o3.o3.o3.o    | * 21 ♦  0  2  10 |  0  1  10  5  20 |  0  5  20 10  20 |  0 10  20 10 10 | 0 10 10 5 2 | 0 5 2 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x. .. .. .. .. ..    | 2  0 | 21  *   * |  5  1   0  0   0 | 10  5   0  0   0 | 10 10   0  0  0 | 5 10  0 0 0 | 1 5 0 0
oo3oo3oo3oo3oo3oo&#x | 1  1 |  * 42   * |  0  1   5  0   0 |  0  5  10  0   0 |  0 10  10  0  0 | 0 10  5 0 0 | 0 5 1 0
.. .x .. .. .. ..    | 0  2 |  *  * 105 |  0  0   1  1   4 |  0  1   4  4   6 |  0  4   6  6  4 | 0  6  4 4 1 | 0 4 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o. .. .. .. ..    | 3  0 |  3  0   0 | 35  *   *  *   * |  4  1   0  0   0 |  6  4   0  0  0 | 4  6  0 0 0 | 1 4 0 0
xo .. .. .. .. ..&#x | 2  1 |  1  2   0 |  * 21   *  *   * ♦  0  5   0  0   0 |  0 10   0  0  0 | 0 10  0 0 0 | 0 5 0 0
.. ox .. .. .. ..&#x | 1  2 |  0  2   1 |  *  * 105  *   * |  0  1   4  0   0 |  0  4   6  0  0 | 0  6  4 0 0 | 0 4 1 0
.o3.x .. .. .. ..    | 0  3 |  0  0   3 |  *  *   * 35   * ♦  0  1   0  4   0 |  0  4   0  6  0 | 0  6  0 4 0 | 0 4 0 1
.. .x3.o .. .. ..    | 0  3 |  0  0   3 |  *  *   *  * 140 |  0  0   1  1   3 |  0  1   3  3  3 | 0  3  3 3 1 | 0 3 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o. .. .. ..    ♦ 4  0 |  6  0   0 |  4  0   0  0   0 | 35  *   *  *   * |  3  1   0  0  0 | 3  3  0 0 0 | 1 3 0 0
xo3ox .. .. .. ..&#x ♦ 3  3 |  3  6   3 |  1  3   3  1   0 |  * 35   *  *   * ♦  0  4   0  0  0 | 0  6  0 0 0 | 0 4 0 0
.. ox3oo .. .. ..&#x ♦ 1  3 |  0  3   3 |  0  0   3  0   1 |  *  * 140  *   * |  0  1   3  0  0 | 0  3  3 0 0 | 0 3 1 0
.o3.x3.o .. .. ..    ♦ 0  6 |  0  0  12 |  0  0   0  4   4 |  *  *   * 35   * ♦  0  1   0  3  0 | 0  3  0 3 0 | 0 3 0 1
.. .x3.o3.o .. ..    ♦ 0  4 |  0  0   6 |  0  0   0  0   4 |  *  *   *  * 105 |  0  0   1  1  2 | 0  1  2 2 1 | 0 2 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o.3o. .. ..    ♦ 5  0 | 10  0   0 | 10  0   0  0   0 |  5  0   0  0   0 | 21  *   *  *  * | 2  1  0 0 0 | 1 2 0 0
xo3ox3oo .. .. ..&#x ♦ 4  6 |  6 12  12 |  4  6  12  4   4 |  1  4   4  1   0 |  * 35   *  *  * | 0  3  0 0 0 | 0 3 0 0
.. ox3oo3oo .. ..&#x ♦ 1  4 |  0  4   6 |  0  0   6  0   4 |  0  0   4  0   1 |  *  * 105  *  * | 0  1  2 0 0 | 0 2 1 0
.o3.x3.o3.o .. ..    ♦ 0 10 |  0  0  30 |  0  0   0 10  20 |  0  0   0  5   5 |  *  *   * 21  * | 0  1  0 2 0 | 0 2 0 1
.. .x3.o3.o3.o ..    ♦ 0  5 |  0  0  10 |  0  0   0  0  10 |  0  0   0  0   5 |  *  *   *  * 42 | 0  0  1 1 1 | 0 1 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o.3o.3o. ..    ♦ 6  0 | 15  0   0 | 20  0   0  0   0 | 15  0   0  0   0 |  6  0   0  0  0 | 7  *  * * * | 1 1 0 0
xo3ox3oo3oo .. ..&#x ♦ 5 10 | 10 20  30 | 10 10  30 10  20 |  5 10  20  5   5 |  1  5   5  1  0 | * 21  * * * | 0 2 0 0
.. ox3oo3oo3oo ..&#x ♦ 1  5 |  0  5  10 |  0  0  10  0  10 |  0  0  10  0   5 |  0  0   5  0  1 | *  * 42 * * | 0 1 1 0
.o3.x3.o3.o3.o ..    ♦ 0 15 |  0  0  60 |  0  0   0 20  60 |  0  0   0 15  30 |  0  0   0  6  6 | *  *  * 7 * | 0 1 0 1
.. .x3.o3.o3.o3.o    ♦ 0  6 |  0  0  15 |  0  0   0  0  20 |  0  0   0  0  15 |  0  0   0  0  6 | *  *  * * 7 | 0 0 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o.3o.3o.3o.    ♦ 7  0 | 21  0   0 | 35  0   0  0   0 | 35  0   0  0   0 | 21  0   0  0  0 | 7  0  0 0 0 | 1 * * *
xo3ox3oo3oo3oo ..&#x ♦ 6 15 | 15 30  60 | 20 15  60 20  60 | 15 20  60 15  30 |  6 15  30  6  6 | 1  6  6 1 0 | * 7 * *
.. ox3oo3oo3oo3oo&#x ♦ 1  6 |  0  6  15 |  0  0  15  0  20 |  0  0  20  0  15 |  0  0  15  0  6 | 0  0  6 0 1 | * * 7 *
.o3.x3.o3.o3.o3.o    ♦ 0 21 |  0  0 105 |  0  0   0 35 140 |  0  0   0 35 105 |  0  0   0 21 42 | 0  0  0 7 7 | * * * 1