Acronym nitarin
Name nit atop rin,
nit-first rotunda of brox
Circumradius sqrt(2) = 1.414214
Lace city
in approx. ASCII-art
o3x3o4o   o3o3x4o   o3x3o4o	-- o3o3x3o4o (nit)
                           
                           
                           
                           
                           
o3o3x4o   o3o3o4q   o3o3x4o	-- o3o3o3x4o (rin)
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign – but last coord. non-negative
Confer
uniform relative:
brox  
general polytopal classes:
segmentopeta   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

oo3oo3xo3ox4oo&#xt   → height = 1/sqrt(2) = 0.707107
(nit || rin)

o.3o.3o.3o.4o.    | 80  *   12   4   0 |  12  12  12   4   0  0 |  4  12  3  12  12  1   0  0 |  4  3  4  12  3  0  0 | 1  4  3 0
.o3.o3.o3.o4.o    |  * 80 |   0   4   8 |   0   0   6   8  12  4 |  0   0  0   4  12  4   8  6 |  0  0  1   8  6  2  4 | 0  2  4 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
.. .. x. .. ..    |  2  0 | 480   *   * |   2   2   1   0   0  0 |  1   4  1   2   2  0   0  0 |  2  2  1   4  1  0  0 | 1  2  2 0
oo3oo3oo3oo4oo&#x |  1  1 |   * 320   * |   0   0   3   2   0  0 |  0   0  0   3   6  1   0  0 |  0  0  1   6  3  0  0 | 0  2  3 0
.. .. .. .x ..    |  0  2 |   *   * 320 |   0   0   0   1   3  1 |  0   0  0   0   3  1   3  3 |  0  0  0   3  3  1  3 | 0  1  3 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
.. o.3x. .. ..    |  3  0 |   3   0   0 | 320   *   *   *   *  * |  1   2  0   1   0  0   0  0 |  2  1  1   2  0  0  0 | 1  2  1 0
.. .. x.3o. ..    |  3  0 |   3   0   0 |   * 320   *   *   *  * |  0   2  1   0   1  0   0  0 |  1  2  0   2  1  0  0 | 1  1  2 0
.. .. xo .. ..&#x |  2  1 |   1   2   0 |   *   * 480   *   *  * |  0   0  0   2   2  0   0  0 |  0  0  1   4  1  0  0 | 0  2  2 0
.. .. .. ox ..&#x |  1  2 |   0   2   1 |   *   *   * 320   *  * |  0   0  0   0   3  1   0  0 |  0  0  0   3  3  0  0 | 0  1  3 0
.. .. .o3.x ..    |  0  3 |   0   0   3 |   *   *   *   * 320  * |  0   0  0   0   1  0   2  1 |  0  0  0   2  1  1  2 | 0  1  2 1
.. .. .. .x4.o    |  0  4 |   0   0   4 |   *   *   *   *   * 80 |  0   0  0   0   0  1   0  3 |  0  0  0   0  3  0  3 | 0  0  3 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
o.3o.3x. .. ..      4  0 |   6   0   0 |   4   0   0   0   0  0 | 80   *  *   *   *  *   *  * |  2  0  1   0  0  0  0 | 1  2  0 0
.. o.3x.3o. ..      6  0 |  12   0   0 |   4   4   0   0   0  0 |  * 160  *   *   *  *   *  * |  1  1  0   1  0  0  0 | 1  1  1 0
.. .. x.3o.4o.      6  0 |  12   0   0 |   0   8   0   0   0  0 |  *   * 40   *   *  *   *  * |  0  2  0   0  1  0  0 | 1  0  2 0
.. oo3xo .. ..&#x   3  1 |   3   3   0 |   1   0   3   0   0  0 |  *   *  * 320   *  *   *  * |  0  0  1   2  0  0  0 | 0  2  1 0
.. .. xo3ox ..&#x   3  3 |   3   6   3 |   0   1   3   3   1  0 |  *   *  *   * 320  *   *  * |  0  0  0   2  1  0  0 | 0  1  2 0
.. .. .. ox4oo&#x   1  4 |   0   4   4 |   0   0   0   4   0  1 |  *   *  *   *   * 80   *  * |  0  0  0   0  3  0  0 | 0  0  3 0
.. .o3.o3.x ..      0  4 |   0   0   6 |   0   0   0   0   4  0 |  *   *  *   *   *  * 160  * |  0  0  0   1  0  1  1 | 0  1  1 1
.. .. .o3.x4.o      0 12 |   0   0  24 |   0   0   0   0   8  6 |  *   *  *   *   *  *   * 40 |  0  0  0   0  1  0  2 | 0  0  2 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
o.3o.3x.3o. ..     10  0 |  30   0   0 |  20  10   0   0   0  0 |  5   5  0   0   0  0   0  0 | 32  *  *   *  *  *  * | 1  1  0 0
.. o.3x.3o.4o.     24  0 |  96   0   0 |  32  64   0   0   0  0 |  0  16  8   0   0  0   0  0 |  * 10  *   *  *  *  * | 1  0  1 0
oo3oo3xo .. ..&#x   4  1 |   6   4   0 |   4   0   6   0   0  0 |  1   0  0   4   0  0   0  0 |  *  * 80   *  *  *  * | 0  2  0 0
.. oo3xo3ox ..&#x   6  4 |  12  12   6 |   4   4  12   6   4  0 |  0   1  0   4   4  0   1  0 |  *  *  * 160  *  *  * | 0  1  1 0
.. .. xo3ox4oo&#x   6 12 |  12  24  24 |   0   8  12  24   8  6 |  0   0  1   0   8  6   0  1 |  *  *  *   * 40  *  * | 0  0  2 0
.o3.o3.o3.x ..      0  5 |   0   0  10 |   0   0   0   0  10  0 |  0   0  0   0   0  0   5  0 |  *  *  *   *  * 32  * | 0  1  0 1
.. .o3.o3.x4.o      0 32 |   0   0  96 |   0   0   0   0  64 24 |  0   0  0   0   0  0  16  8 |  *  *  *   *  *  * 10 | 0  0  1 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
o.3o.3x.3o.4o.     80  0 | 480   0   0 | 320 320   0   0   0  0 | 80 160 40   0   0  0   0  0 | 32 10  0   0  0  0  0 | 1  *  * *
oo3oo3xo3ox ..&#x  10  5 |  30  20  10 |  20  10  30  10  10  0 |  5   5  0  20  10  0   5  0 |  1  0  5   5  0  1  0 | * 32  * *
.. oo3xo3ox4oo&#x  24 32 |  96  96  96 |  32  64  96  96  64 24 |  0  16  8  32  64 24  16  8 |  0  1  0  16  8  0  1 | *  * 10 *
.o3.o3.o3.x4.o      0 80 |   0   0 320 |   0   0   0   0 320 80 |  0   0  0   0   0  0 160 40 |  0  0  0   0  0 32 10 | *  *  * 1

ox3xo3ox *b3oo3oo&#x   → height = 1/sqrt(2) = 0.707107
(nit || rin)

o.3o.3o. *b3o.3o.    | 80  *   12   4   0   0 |   6   6  12   2  12   2   0  0   0 |  3  6  6  4   6  1   6  12  0  0  0 |  3  2  2  3  6  6  4  0  0  0 | 1  3  2  2 0
.o3.o3.o *b3.o3.o    |  * 80 |   0   4   4   4 |   0   0   0   4   6   4   6  4   6 |  0  0  0  0   6  4   6   4  6  4  4 |  0  0  0  6  4  4  1  4  1  1 | 0  4  1  1 1
---------------------+-------+-----------------+------------------------------------+-------------------------------------+-------------------------------+-------------
.. x. ..    .. ..    |  2  0 | 480   *   *   * |   1   1   2   0   1   0   0  0   0 |  1  2  2  1   1  0   1   2  0  0  0 |  2  1  1  1  2  2  1  0  0  0 | 1  2  1  1 0
oo3oo3oo *b3oo3oo&#x |  1  1 |   * 320   *   * |   0   0   0   1   3   1   0  0   0 |  0  0  0  0   3  1   3   3  0  0  0 |  0  0  0  3  3  3  1  0  0  0 | 0  3  1  1 0
.x .. ..    .. ..    |  0  2 |   *   * 160   * |   0   0   0   1   0   0   3  1   0 |  0  0  0  0   3  1   0   0  3  3  0 |  0  0  0  3  3  0  0  3  1  0 | 0  3  1  0 1
.. .. .x    .. ..    |  0  2 |   *   *   * 160 |   0   0   0   0   0   1   0  1   3 |  0  0  0  0   0  1   3   0  3  0  3 |  0  0  0  3  0  3  0  3  0  1 | 0  3  0  1 1
---------------------+-------+-----------------+------------------------------------+-------------------------------------+-------------------------------+-------------
o.3x. ..    .. ..    |  3  0 |   3   0   0   0 | 160   *   *   *   *   *   *  *   * |  1  2  0  0   1  0   0   0  0  0  0 |  2  1  0  1  2  0  0  0  0  0 | 1  2  1  0 0
.. x.3o.    .. ..    |  3  0 |   3   0   0   0 |   * 160   *   *   *   *   *  *   * |  1  0  2  0   0  0   1   0  0  0  0 |  2  0  1  1  0  2  0  0  0  0 | 1  2  0  1 0
.. x. .. *b3o. ..    |  3  0 |   3   0   0   0 |   *   * 320   *   *   *   *  *   * |  0  1  1  1   0  0   0   1  0  0  0 |  1  1  1  0  1  1  1  0  0  0 | 1  1  1  1 0
ox .. ..    .. ..&#x |  1  2 |   0   2   1   0 |   *   *   * 160   *   *   *  *   * |  0  0  0  0   3  1   0   0  0  0  0 |  0  0  0  3  3  0  0  0  0  0 | 0  3  1  0 0
.. xo ..    .. ..&#x |  2  1 |   1   2   0   0 |   *   *   *   * 480   *   *  *   * |  0  0  0  0   1  0   1   2  0  0  0 |  0  0  0  1  2  2  1  0  0  0 | 0  2  1  1 0
.. .. ox    .. ..&#x |  1  2 |   0   2   0   1 |   *   *   *   *   * 160   *  *   * |  0  0  0  0   0  1   3   0  0  0  0 |  0  0  0  3  0  3  0  0  0  0 | 0  3  0  1 0
.x3.o ..    .. ..    |  0  3 |   0   0   3   0 |   *   *   *   *   *   * 160  *   * |  0  0  0  0   1  0   0   0  1  2  0 |  0  0  0  1  2  0  0  2  1  0 | 0  2  1  0 1
.x .. .x    .. ..    |  0  4 |   0   0   2   2 |   *   *   *   *   *   *   * 80   * |  0  0  0  0   0  1   0   0  3  0  0 |  0  0  0  3  0  0  0  3  0  0 | 0  3  0  0 1
.. .o3.x    .. ..    |  0  3 |   0   0   0   3 |   *   *   *   *   *   *   *  * 160 |  0  0  0  0   0  0   1   0  1  0  2 |  0  0  0  1  0  2  0  2  0  1 | 0  2  0  1 1
---------------------+-------+-----------------+------------------------------------+-------------------------------------+-------------------------------+-------------
o.3x.3o.    .. ..      6  0 |  12   0   0   0 |   4   4   0   0   0   0   0  0   0 | 40  *  *  *   *  *   *   *  *  *  * |  2  0  0  1  0  0  0  0  0  0 | 1  2  0  0 0
o.3x. .. *b3o. ..      6  0 |  12   0   0   0 |   4   0   4   0   0   0   0  0   0 |  * 80  *  *   *  *   *   *  *  *  * |  1  1  0  0  1  0  0  0  0  0 | 1  1  1  0 0
.. x.3o. *b3o. ..      6  0 |  12   0   0   0 |   0   4   4   0   0   0   0  0   0 |  *  * 80  *   *  *   *   *  *  *  * |  1  0  1  0  0  1  0  0  0  0 | 1  1  0  1 0
.. x. .. *b3o.3o.      4  0 |   6   0   0   0 |   0   0   4   0   0   0   0  0   0 |  *  *  * 80   *  *   *   *  *  *  * |  0  1  1  0  0  0  1  0  0  0 | 1  0  1  1 0
ox3xo ..    .. ..&#x   3  3 |   3   6   3   0 |   1   0   0   3   3   0   1  0   0 |  *  *  *  * 160  *   *   *  *  *  * |  0  0  0  1  2  0  0  0  0  0 | 0  2  1  0 0
ox .. ox    .. ..&#x   1  4 |   0   4   2   2 |   0   0   0   2   0   2   0  1   0 |  *  *  *  *   * 80   *   *  *  *  * |  0  0  0  3  0  0  0  0  0  0 | 0  3  0  0 0
.. xo3ox    .. ..&#x   3  3 |   3   6   0   3 |   0   1   0   0   3   3   0  0   1 |  *  *  *  *   *  * 160   *  *  *  * |  0  0  0  1  0  2  0  0  0  0 | 0  2  0  1 0
.. xo .. *b3oo ..&#x   3  1 |   3   3   0   0 |   0   0   1   0   3   0   0  0   0 |  *  *  *  *   *  *   * 320  *  *  * |  0  0  0  0  1  1  1  0  0  0 | 0  1  1  1 0
.x3.o3.x    .. ..      0 12 |   0   0  12  12 |   0   0   0   0   0   0   4  6   4 |  *  *  *  *   *  *   *   * 40  *  * |  0  0  0  1  0  0  0  2  0  0 | 0  2  0  0 1
.x3.o .. *b3.o ..      0  4 |   0   0   6   0 |   0   0   0   0   0   0   4  0   0 |  *  *  *  *   *  *   *   *  * 80  * |  0  0  0  0  1  0  0  1  1  0 | 0  1  1  0 1
.. .o3.x *b3.o ..      0  4 |   0   0   0   6 |   0   0   0   0   0   0   0  0   4 |  *  *  *  *   *  *   *   *  *  * 80 |  0  0  0  0  0  1  0  1  0  1 | 0  1  0  1 1
---------------------+-------+-----------------+------------------------------------+-------------------------------------+-------------------------------+-------------
o.3x.3o. *b3o. ..     24  0 |  96   0   0   0 |  32  32  32   0   0   0   0  0   0 |  8  8  8  0   0  0   0   0  0  0  0 | 10  *  *  *  *  *  *  *  *  * | 1  1  0  0 0
o.3x. .. *b3o.3o.     10  0 |  30   0   0   0 |  10   0  20   0   0   0   0  0   0 |  0  5  0  5   0  0   0   0  0  0  0 |  * 16  *  *  *  *  *  *  *  * | 1  0  1  0 0
.. x.3o. *b3o.3o.     10  0 |  30   0   0   0 |   0  10  20   0   0   0   0  0   0 |  0  0  5  5   0  0   0   0  0  0  0 |  *  * 16  *  *  *  *  *  *  * | 1  0  0  1 0
ox3xo3ox    .. ..&#x   6 12 |  12  24  12  12 |   4   4   0  12  12  12   4  6   4 |  1  0  0  0   4  6   4   0  1  0  0 |  *  *  * 40  *  *  *  *  *  * | 0  2  0  0 0
ox3xo .. *b3oo ..&#x   6  4 |  12  12   6   0 |   4   0   4   6  12   0   4  0   0 |  0  1  0  0   4  0   0   4  0  1  0 |  *  *  *  * 80  *  *  *  *  * | 0  1  1  0 0
.. xo3ox *b3oo ..&#x   6  4 |  12  12   0   6 |   0   4   4   0  12   6   0  0   4 |  0  0  1  0   0  0   4   4  0  0  1 |  *  *  *  *  * 80  *  *  *  * | 0  1  0  1 0
.. xo .. *b3oo3oo&#x   4  1 |   6   4   0   0 |   0   0   4   0   6   0   0  0   0 |  0  0  0  1   0  0   0   4  0  0  0 |  *  *  *  *  *  * 80  *  *  * | 0  0  1  1 0
.x3.o3.x *b3.o ..      0 32 |   0   0  48  48 |   0   0   0   0   0   0  32 24  32 |  0  0  0  0   0  0   0   0  8  8  8 |  *  *  *  *  *  *  * 10  *  * | 0  1  0  0 1
.x3.o .. *b3.o3.o      0  5 |   0   0  10   0 |   0   0   0   0   0   0  10  0   0 |  0  0  0  0   0  0   0   0  0  5  0 |  *  *  *  *  *  *  *  * 16  * | 0  0  1  0 1
.. .o3.x *b3.o3.o      0  5 |   0   0   0  10 |   0   0   0   0   0   0   0  0  10 |  0  0  0  0   0  0   0   0  0  0  5 |  *  *  *  *  *  *  *  *  * 16 | 0  0  0  1 1
---------------------+-------+-----------------+------------------------------------+-------------------------------------+-------------------------------+-------------
o.3x.3o. *b3o.3o.     80  0 | 480   0   0   0 | 160 160 320   0   0   0   0  0   0 | 40 80 80 80   0  0   0   0  0  0  0 | 10 16 16  0  0  0  0  0  0  0 | 1  *  *  * *
ox3xo3ox *b3oo ..&#x  24 32 |  96  96  48  48 |  32  32  32  48  96  48  32 24  32 |  8  8  8  0  32 24  32  32  8  8  8 |  1  0  0  8  8  8  0  1  0  0 | * 10  *  * *
ox3xo .. *b3oo3oo&#x  10  5 |  30  20  10   0 |  10   0  20  10  30   0  10  0   0 |  0  5  0  5  10  0   0  20  0  5  0 |  0  1  0  0  5  0  5  0  1  0 | *  * 16  * *
.. xo3ox *b3oo3oo&#x  10  5 |  30  20   0  10 |   0  10  20   0  30  10   0  0  10 |  0  0  5  5   0  0  10  20  0  0  5 |  0  0  1  0  0  5  5  0  0  1 | *  *  * 16 *
.x3.o3.x *b3.o3.o      0 80 |   0   0 160 160 |   0   0   0   0   0   0 160 80 160 |  0  0  0  0   0  0   0   0 40 80 80 |  0  0  0  0  0  0  0 10 16 16 | *  *  *  * 1

© 2004-2019
top of page