Acronym roc
Name rectified octaexon,
vertex figure of hocto,
Gosset polytope 05,1
Circumradius sqrt(3)/2 = 0.866025
Confer
related segmentoexa:
octatetdip  
general polytopal classes:
segmentoexa   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

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

oxo3xoo3ooo oxo3oox3ooo&#xt   → both heights = 1/2
(oct || pseudo tetdip || ortho oct)

o..3o..3o.. o..3o..3o..     & | 12  *   4  8  0 | 2 2  4 16  12  0 | 1  8  6  8  24  8 0 | 4 16 12 16  2 |  7  8  8  4 | 6 2
.o.3.o.3.o. .o.3.o.3.o.       |  * 16   0  6  6 | 0 0  6  6  18  6 | 0  6  9  2  18 18 2 | 2 18  6 18  6 |  6  9  6  6 | 6 2
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
... x.. ... ... ... ...     & |  2  0 | 24  *  * | 1 1  0  4   0  0 | 1  4  0  4   6  0 0 | 4  6  6  4  0 |  6  4  4  1 | 5 1
oo.3oo.3oo. oo.3oo.3oo.&#x  & |  1  1 |  * 96  * | 0 0  1  2   3  0 | 0  2  3  1   6  3 0 | 1  9  3  6  1 |  4  6  3  2 | 5 1
.x. ... ... ... ... ...     & |  0  2 |  *  * 48 | 0 0  1  0   3  2 | 0  2  3  0   3  6 1 | 1  9  1  6  3 |  4  6  2  3 | 5 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
o..3x.. ... ... ... ...     & |  3  0 |  3  0  0 | 8 *  *  *   *  *  1  4  0  0   0  0 0 | 4  6  0  0  0 |  6  4  0  0 | 5 0
... x..3o.. ... ... ...     & |  3  0 |  3  0  0 | * 8  *  *   *  * | 1  0  0  4   0  0 0 | 4  0  6  0  0 |  6  0  4  0 | 4 1
ox. ... ... ... ... ...&#x  & |  1  2 |  0  2  1 | * * 48  *   *  *  0  2  3  0   0  0 0 | 1  9  0  0  0 |  4  6  0  0 | 5 0
... xo. ... ... ... ...&#x  & |  2  1 |  1  2  0 | * *  * 96   *  * | 0  1  0  1   3  0 0 | 1  3  3  3  0 |  3  3  3  1 | 4 1
... ... ... ox. ... ...&#x  & |  1  2 |  0  2  1 | * *  *  * 144  * | 0  0  1  0   2  2 0 | 0  4  1  4  1 |  2  3  2  2 | 4 1
.x.3.o. ... ... ... ...     & |  0  3 |  0  0  3 | * *  *  *   * 32 | 0  1  0  0   0  3 1 | 1  3  0  3  3 |  3  3  1  3 | 4 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
o..3x..3o.. ... ... ...     &   6  0 | 12  0  0 | 4 4  0  0   0  0 | 2  *  *  *   *  * *  4  0  0  0  0 |  6  0  0  0 | 4 0
ox.3xo. ... ... ... ...&#x  &   3  3 |  3  6  3 | 1 0  3  3   0  1 | * 32  *  *   *  * *  1  3  0  0  0 |  3  3  0  0 | 4 0
oxo ... ... oxo ... ...&#xt     2  4 |  0  8  4 | 0 0  4  0   4  0 | *  * 36  *   *  * *  0  4  0  0  0 |  2  4  0  0 | 4 0
... xo.3oo. ... ... ...&#x  &   3  1 |  3  3  0 | 0 1  0  3   0  0 | *  *  * 32   *  * * | 1  0  3  0  0 |  3  0  3  0 | 3 1
... xo. ... ox. ... ...&#x  &   2  2 |  1  4  1 | 0 0  0  2   2  0 | *  *  *  * 144  * * | 0  1  1  2  0 |  1  2  2  1 | 3 1
... ... ... ox.3oo. ...&#x  &   1  3 |  0  3  3 | 0 0  0  0   3  1 | *  *  *  *   * 96 * | 0  1  0  2  1 |  1  2  1  2 | 3 1
.x.3.o.3.o. ... ... ...     &   0  4 |  0  0  6 | 0 0  0  0   0  4 | *  *  *  *   *  * 8 | 1  0  0  0  3 |  3  0  0  3 | 3 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
ox.3xo.3oo. ... ... ...&#x  &   6  4 | 12 12  6 | 4 4  6 12   0  4 | 1  4  0  4   0  0 1 | 8  *  *  *  * |  3  0  0  0 | 3 0
oxo3xoo ... oxo ... ...&#xt &   4  6 |  3 18  9 | 1 0  9  6  12  2 | 0  2  3  0   3  2 0 | * 48  *  *  * |  1  2  0  0 | 3 0
... xo.3oo. ox. ... ...&#x  &   3  2 |  3  6  1 | 0 1  0  6   3  0 | 0  0  0  2   3  0 0 | *  * 48  *  * |  1  0  2  0 | 2 1
... xo. ... ox.3oo. ...&#x  &   2  3 |  1  6  3 | 0 0  0  3   6  1 | 0  0  0  0   3  2 0 | *  *  * 96  * |  0  1  1  1 | 2 1
... ... ... ox.3oo.3oo.&#x  &   1  4 |  0  4  6 | 0 0  0  0   6  4 | 0  0  0  0   0  4 1 | *  *  *  * 24 |  1  0  0  2 | 2 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
oxo3xoo3ooo oxo ... ...&#xt &   7  8 | 12 32 16 | 4 4 16 24  24  8 | 1  8  6  8  12  8 2 | 2  4  4  0  2 | 12  *  *  * | 2 0
oxo3xoo ... oxo3oox ...&#xt     6  9 |  6 36 18 | 2 0 18 18  36  6 | 0  6  9  0  18 12 0 | 0  6  0  6  0 |  * 16  *  * | 2 0
... xo.3oo. ox.3oo. ...&#x  &   3  3 |  3  9  3 | 0 1  0  9   9  1 | 0  0  0  3   9  3 0 | 0  0  3  3  0 |  *  * 32  * | 1 1
... xo. ... ox.3oo.3oo.&#x  &   2  4 |  1  8  6 | 0 0  0  4  12  4 | 0  0  0  0   6  8 1 | 0  0  0  4  2 |  *  *  * 24 | 1 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
oxo3xoo3ooo oxo3oox ...&#xt &   9 12 | 15 60 30 | 5 4 30 48  72 16 | 1 16 18 12  54 36 3 | 3 18 12 24  6 |  3  4  4  3 | 8 *
... xo.3oo. ox.3oo.3oo.&#x  &   3  4 |  3 12  6 | 0 1  0 12  18  4 | 0  0  0  4  18 12 1 | 0  0  6 12  3 |  0  0  4  3 | * 8

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