Acronym cytaxh
Name cyclotruncated hexateric honeycomb
Confer
more general:
xPo3o...o3oPxQ*a  
External
links
wikipedia

By virtue of an outer symmetry this is a non-quasiregular monotoxal pentacomb, that is all edges belong to the same equivalence class.


Incidence matrix according to Dynkin symbol

x3x3o3o3o3o3*a   (N → ∞)

. . . . . .    | 6N |   5   5 |  20  10  10 |  30  30  10  10 | 20 30 20  5  5 | 5 10 10 5 1 1
---------------+----+---------+-------------+-----------------+----------------+--------------
x . . . . .    |  2 | 15N   * |   4   4   0 |   6  12   6   0 |  4 12 12  4  0 | 1  4  6 4 1 0
. x . . . .    |  2 |   * 15N |   4   0   4 |  12   6   0   6 | 12 12  4  0  4 | 4  6  4 1 0 1
---------------+----+---------+-------------+-----------------+----------------+--------------
x3x . . . .    |  6 |   3   3 | 20N   *   * |   3   3   0   0 |  3  6  3  0  0 | 1  3  3 1 0 0
x . . . . o3*a |  3 |   3   0 |   * 20N   * |   0   3   3   0 |  0  3  6  3  0 | 0  1  3 3 1 0
. x3o . . .    |  3 |   0   3 |   *   * 20N |   3   0   0   3 |  6  3  0  0  3 | 3  3  1 0 0 1
---------------+----+---------+-------------+-----------------+----------------+--------------
x3x3o . . .     12 |   6  12 |   4   0   4 | 15N   *   *   * |  2  2  0  0  0 | 1  2  1 0 0 0
x3x . . . o3*a  12 |  12   6 |   4   4   0 |   * 15N   *   * |  0  2  2  0  0 | 0  1  2 1 0 0
x . . . o3o3*a   4 |   6   0 |   0   4   0 |   *   * 15N   * |  0  0  2  2  0 | 0  0  1 2 1 0
. x3o3o . .      4 |   0   6 |   0   0   4 |   *   *   * 15N |  2  0  0  0  2 | 2  1  0 0 0 1
---------------+----+---------+-------------+-----------------+----------------+--------------
x3x3o3o . .     20 |  10  30 |  10   0  20 |   5   0   0   5 | 6N  *  *  *  * | 1  1  0 0 0 0
x3x3o . . o3*a  30 |  30  30 |  20  10  10 |   5   5   0   0 |  * 6N  *  *  * | 0  1  1 0 0 0
x3x . . o3o3*a  20 |  30  10 |  10  20   0 |   0   5   5   0 |  *  * 6N  *  * | 0  0  1 1 0 0
x . . o3o3o3*a   5 |  10   0 |   0  10   0 |   0   0   5   0 |  *  *  * 6N  * | 0  0  0 1 1 0
. x3o3o3o .      5 |   0  10 |   0   0  10 |   0   0   0   5 |  *  *  *  * 6N | 1  0  0 0 0 1
---------------+----+---------+-------------+-----------------+----------------+--------------
x3x3o3o3o .     30 |  15  60 |  20   0  60 |  15   0   0  30 |  6  0  0  0  6 | N  *  * * * *
x3x3o3o . o3*a  60 |  60  90 |  60  20  60 |  30  15   0  15 |  6  6  0  0  0 | *  N  * * * *
x3x3o . o3o3*a  60 |  90  60 |  60  60  20 |  15  30  15   0 |  0  6  6  0  0 | *  *  N * * *
x3x . o3o3o3*a  30 |  60  15 |  20  60   0 |   0  15  30   0 |  0  0  6  6  0 | *  *  * N * *
x . o3o3o3o3*a   6 |  15   0 |   0  20   0 |   0   0  15   0 |  0  0  0  6  0 | *  *  * * N *
. x3o3o3o3o      6 |   0  15 |   0   0  20 |   0   0   0  15 |  0  0  0  0  6 | *  *  * * * N
or
. . . . . .       | 3N |  10 |  20  20 |  60  20 | 40 30 10 | 10 20 2
------------------+----+-----+---------+---------+----------+--------
x . . . . .     & |  2 | 15N |   4   4 |  18   6 | 16 12  4 |  5 10 1
------------------+----+-----+---------+---------+----------+--------
x3x . . . .       |  6 |   6 | 10N   * |   6   0 |  6  6  0 |  2  6 0
x . . . . o3*a  & |  3 |   3 |   * 20N |   3   3 |  6  3  3 |  3  4 1
------------------+----+-----+---------+---------+----------+--------
x3x3o . . .     &  12 |  18 |   4   4 | 15N   * |  2  2  0 |  1  3 0
x . . . o3o3*a  &   4 |   6 |   0   4 |   * 15N |  2  0  2 |  2  1 1
------------------+----+-----+---------+---------+----------+--------
x3x3o3o . .     &  20 |  40 |  10  20 |   5   5 | 6N  *  * |  1  1 0
x3x3o . . o3*a     30 |  60 |  20  20 |  10   0 |  * 3N  * |  0  2 0
x . . o3o3o3*a  &   5 |  10 |   0  10 |   0   5 |  *  * 6N |  1  0 1
------------------+----+-----+---------+---------+----------+--------
x3x3o3o3o .     &  30 |  75 |  20  60 |  15  30 |  6  0  6 |  N  * *
x3x3o3o . o3*a  &  60 | 150 |  60  80 |  45  15 |  6  6  0 |  *  N *
x . o3o3o3o3*a  &   6 |  15 |   0  20 |   0  15 |  0  0  6 |  *  * N

© 2004-2024
top of page