Acronym ratanit
Name rectified triacontaditeron atop penteractitriacontiditeron,
rat-first rotunda of brag
Circumradius sqrt(3/2) = 1.224745
Lace city
in approx. ASCII-art
h   i   h		- o3x3o3o4o (rat)
         
i   r   i		- o3o3x3o4o (nit)


where:
h - x3o3o4o (hex)
i - o3x3o4o (ico)
r - o3o3x4o (rit)
Confer
uniform relative:
brag  
general polytopal classes:
segmentopeta   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

oo3xo3ox3oo4oo&#x   → height = 1/sqrt(2) = 0.707107
(rat || nit)

o.3o.3o.3o.4o.    | 40  *   12   6   0 |  6  24  12  12   0   0 | 12  16  6  24   8  0   0  0 |  8  2 12  16  1  0  0 | 1  8  2 0
.o3.o3.o3.o4.o    |  * 80 |   0   3  12 |  0   0   3  12  12  12 |  0   0  1  12  12  4  12  3 |  0  0  4  12  3  4  3 | 0  4  3 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
.. x. .. .. ..    |  2  0 | 240   *   * |  1   4   1   0   0   0 |  4   4  1   4   0  0   0  0 |  4  1  4   4  0  0  0 | 1  4  1 0
oo3oo3oo3oo4oo&#x |  1  1 |   * 240   * |  0   0   2   4   0   0 |  0   0  1   8   4  0   0  0 |  0  0  4   8  1  0  0 | 0  4  2 0
.. .. .x .. ..    |  0  2 |   *   * 480 |  0   0   0   1   2   2 |  0   0  0   2   2  1   4  1 |  0  0  1   4  1  2  2 | 0  2  2 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
o.3x. .. .. ..    |  3  0 |   3   0   0 | 80   *   *   *   *   * |  4   0  1   0   0  0   0  0 |  4  0  4   0  0  0  0 | 1  4  0 0
.. x.3o. .. ..    |  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
.. xo .. .. ..&#x |  2  1 |   1   2   0 |  *   * 240   *   *   * |  0   0  1   4   0  0   0  0 |  0  0  4   4  0  0  0 | 0  4  1 0
.. .. ox .. ..&#x |  1  2 |   0   2   1 |  *   *   * 480   *   * |  0   0  0   2   2  0   0  0 |  0  0  1   4  1  0  0 | 0  2  2 0
.. .o3.x .. ..    |  0  3 |   0   0   3 |  *   *   *   * 320   * |  0   0  0   1   0  1   2  0 |  0  0  1   2  0  2  1 | 0  2  1 1
.. .. .x3.o ..    |  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
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
o.3x.3o. .. ..      6  0 |  12   0   0 |  4   4   0   0   0   0 | 80   *  *   *   *  *   *  * |  2  0  1   0  0  0  0 | 1  2  0 0
.. x.3o.3o. ..      4  0 |   6   0   0 |  0   4   0   0   0   0 |  * 160  *   *   *  *   *  * |  1  1  0   1  0  0  0 | 1  1  1 0
oo3xo .. .. ..&#x   3  1 |   3   3   0 |  1   0   3   0   0   0 |  *   * 80   *   *  *   *  * |  0  0  4   0  0  0  0 | 0  4  0 0
.. xo3ox .. ..&#x   3  3 |   3   6   3 |  0   1   3   3   1   0 |  *   *  * 320   *  *   *  * |  0  0  1   2  0  0  0 | 0  2  1 0
.. .. ox3oo ..&#x   1  3 |   0   3   3 |  0   0   0   3   0   1 |  *   *  *   * 320  *   *  * |  0  0  0   2  1  0  0 | 0  1  2 0
.o3.o3.x .. ..      0  4 |   0   0   6 |  0   0   0   0   4   0 |  *   *  *   *   * 80   *  * |  0  0  1   0  0  2  0 | 0  2  0 1
.. .o3.x3.o ..      0  6 |   0   0  12 |  0   0   0   0   4   4 |  *   *  *   *   *  * 160  * |  0  0  0   1  0  1  1 | 0  1  1 1
.. .. .x3.o4.o      0  6 |   0   0  12 |  0   0   0   0   0   8 |  *   *  *   *   *  *   * 40 |  0  0  0   0  1  0  2 | 0  0  2 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
o.3x.3o.3o. ..     10  0 |  30   0   0 | 10  20   0   0   0   0 |  5   5  0   0   0  0   0  0 | 32  *  *   *  *  *  * | 1  1  0 0
.. x.3o.3o.4o.      8  0 |  24   0   0 |  0  32   0   0   0   0 |  0  16  0   0   0  0   0  0 |  * 10  *   *  *  *  * | 1  0  1 0
oo3xo3ox .. ..&#x   6  4 |  12  12   6 |  4   4  12   6   4   0 |  1   0  4   4   0  1   0  0 |  *  * 80   *  *  *  * | 0  2  0 0
.. xo3ox3oo ..&#x   4  6 |   6  12  12 |  0   4   6  12   4   4 |  0   1  0   4   4  0   1  0 |  *  *  * 160  *  *  * | 0  1  1 0
.. .. ox3oo4oo&#x   1  6 |   0   6  12 |  0   0   0  12   0   8 |  0   0  0   0   8  0   0  1 |  *  *  *   * 40  *  * | 0  0  2 0
.o3.o3.x.o ..       0 10 |   0   0  30 |  0   0   0   0  20  10 |  0   0  0   0   0  5   5  0 |  *  *  *   *  * 32  * | 0  1  0 1
.. .o3.x.o4.o       0 24 |   0   0  96 |  0   0   0   0  32  64 |  0   0  0   0   0  0  16  8 |  *  *  *   *  *  * 10 | 0  0  1 1
------------------+-------+-------------+------------------------+-----------------------------+-----------------------+----------
o.3x.3o.3o.4o.     40  0 | 240   0   0 | 80 320   0   0   0   0 | 80 160  0   0   0  0   0  0 | 32 10  0   0  0  0  0 | 1  *  * *
oo3xo3ox3oo ..&#x  10 10 |  30  30  30 | 10  20  30  30  20  10 |  5   5 10  20  10  5   5  0 |  1  0  5   5  0  1  0 | * 32  * *
.. xo3ox3oo4oo&#x   8 24 |  24  48  96 |  0  32  24  96  32  64 |  0  16  0  32  64  0  16  8 |  0  1  0  16  8  0  1 | *  * 10 *
.o3.o3.x3.o4.o      0 80 |   0   0 480 |  0   0   0   0 320 320 |  0   0  0   0   0 80 160 40 |  0  0  0   0  0 32 10 | *  *  * 1

oo3ox3oo *b3xo3oo&#x   → height = 1/sqrt(2) = 0.707107
(rat || nit)

o.3o.3o. *b3o.3o.    | 40  *   12   6   0 |  24  6  12  12   0   0   0 |  8  8 12   4   4  24  6  0  0  0  0 |  2  4  4  1  8  8 12  0  0  0 | 1  2  4  4 0
.o3.o3.o *b3.o3.o    |  * 80 |   0   3  12 |   0  0  12   3   6   6  12 |  0  0  0   6   6  12  1  3  6  6  4 |  0  0  0  3  6  6  4  3  2  2 | 0  3  2  2 1
---------------------+-------+-------------+----------------------------+-------------------------------------+-------------------------------+-------------
.. .. ..    x. ..    |  2  0 | 240   *   * |   4  1   0   1   0   0   0 |  2  2  4   0   0   4  1  0  0  0  0 |  1  2  2  0  2  2  4  0  0  0 | 1  1  2  2 0
oo3oo3oo *b3oo3oo&#x |  1  1 |   * 240   * |   0  0   4   4   0   0   0 |  0  0  0   2   2   8  1  0  0  0  0 |  0  0  0  1  4  4  4  0  0  0 | 0  2  2  2 0
.. .x ..    .. ..    |  0  2 |   *   * 480 |   0  0   1   0   1   1   2 |  0  0  0   1   1   2  0  1  2  2  1 |  0  0  0  1  2  2  1  2  1  1 | 0  2  1  1 1
---------------------+-------+-------------+----------------------------+-------------------------------------+-------------------------------+-------------
.. o. .. *b3x. ..    |  3  0 |   3   0   0 | 320  *   *   *   *   *   * |  1  1  1   0   0   1  0  0  0  0  0 |  1  1  1  0  1  1  1  0  0  0 | 1  1  1  1 0
.. .. ..    x.3o.    |  3  0 |   3   0   0 |   * 80   *   *   *   *   * |  0  0  4   0   0   0  1  0  0  0  0 |  0  2  2  0  0  0  4  0  0  0 | 1  0  2  2 0
.. ox ..    .. ..&#x |  1  2 |   0   2   1 |   *  * 480   *   *   *   * |  0  0  0   1   1   2  0  0  0  0  0 |  0  0  0  1  2  2  1  0  0  0 | 0  2  1  1 0
.. .. ..    xo ..&#x |  2  1 |   1   2   0 |   *  *   * 240   *   *   * |  0  0  0   0   0   4  1  0  0  0  0 |  0  0  0  0  2  2  4  0  0  0 | 0  1  2  2 0
.o3.x ..    .. ..    |  0  3 |   0   0   3 |   *  *   *   * 160   *   * |  0  0  0   1   0   0  0  1  2  0  0 |  0  0  0  1  2  0  0  2  1  0 | 0  2  1  0 1
.. .x3.o    .. ..    |  0  3 |   0   0   3 |   *  *   *   *   * 160   * |  0  0  0   0   1   0  0  1  0  2  0 |  0  0  0  1  0  2  0  2  0  1 | 0  2  0  1 1
.. .x .. *b3.o ..    |  0  3 |   0   0   3 |   *  *   *   *   *   * 320 |  0  0  0   0   0   1  0  0  1  1  1 |  0  0  0  0  1  1  1  1  1  1 | 0  1  1  1 1
---------------------+-------+-------------+----------------------------+-------------------------------------+-------------------------------+-------------
o.3o. .. *b3x. ..      4  0 |   6   0   0 |   4  0   0   0   0   0   0 | 80  *  *   *   *   *  *  *  *  *  * |  1  1  0  0  1  0  0  0  0  0 | 1  1  1  0 0
.. o.3o. *b3x. ..      4  0 |   6   0   0 |   4  0   0   0   0   0   0 |  * 80  *   *   *   *  *  *  *  *  * |  1  0  1  0  0  1  0  0  0  0 | 1  1  0  1 0
.. o. .. *b3x.3o.      6  0 |  12   0   0 |   4  4   0   0   0   0   0 |  *  * 80   *   *   *  *  *  *  *  * |  0  1  1  0  0  0  1  0  0  0 | 1  0  1  1 0
oo3ox ..    .. ..&#x   1  3 |   0   3   3 |   0  0   3   0   1   0   0 |  *  *  * 160   *   *  *  *  *  *  * |  0  0  0  1  2  0  0  0  0  0 | 0  2  1  0 0
.. ox3oo    .. ..&#x   1  3 |   0   3   3 |   0  0   3   0   0   1   0 |  *  *  *   * 160   *  *  *  *  *  * |  0  0  0  1  0  2  0  0  0  0 | 0  2  0  1 0
.. ox .. *b3xo ..&#x   3  3 |   3   6   3 |   1  0   3   3   0   0   1 |  *  *  *   *   * 320  *  *  *  *  * |  0  0  0  0  1  1  1  0  0  0 | 0  1  1  1 0
.. .. ..    xo3oo&#x   3  1 |   3   3   0 |   0  1   0   3   0   0   0 |  *  *  *   *   *   * 80  *  *  *  * |  0  0  0  0  0  0  4  0  0  0 | 0  0  2  2 0
.o3.x3.o    .. ..      0  6 |   0   0  12 |   0  0   0   0   4   4   0 |  *  *  *   *   *   *  * 40  *  *  * |  0  0  0  1  0  0  0  2  0  0 | 0  2  0  0 1
.o3.x .. *b3.o ..      0  6 |   0   0  12 |   0  0   0   0   4   0   4 |  *  *  *   *   *   *  *  * 80  *  * |  0  0  0  0  1  0  0  1  1  0 | 0  1  1  0 1
.. .x3.o *b3.o ..      0  6 |   0   0  12 |   0  0   0   0   0   4   4 |  *  *  *   *   *   *  *  *  * 80  * |  0  0  0  0  0  1  0  1  0  1 | 0  1  0  1 1
.. .x .. *b3.o3.o      0  4 |   0   0   6 |   0  0   0   0   0   0   4 |  *  *  *   *   *   *  *  *  *  * 80 |  0  0  0  0  0  0  1  0  1  1 | 0  0  1  1 1
---------------------+-------+-------------+----------------------------+-------------------------------------+-------------------------------+-------------
o.3o.3o. *b3x. ..      8  0 |  24   0   0 |  32  0   0   0   0   0   0 |  8  8  0   0   0   0  0  0  0  0  0 | 10  *  *  *  *  *  *  *  *  * | 1  1  0  0 0
o.3o. .. *b3x.3o.     10  0 |  30   0   0 |  20 10   0   0   0   0   0 |  5  0  5   0   0   0  0  0  0  0  0 |  * 16  *  *  *  *  *  *  *  * | 1  0  1  0 0
.. o.3o. *b3x.3o.     10  0 |  30   0   0 |  20 10   0   0   0   0   0 |  0  5  5   0   0   0  0  0  0  0  0 |  *  * 16  *  *  *  *  *  *  * | 1  0  0  1 0
oo3ox3oo    .. ..&#x   1  6 |   0   6  12 |   0  0  12   0   4   4   0 |  0  0  0   4   4   0  0  1  0  0  0 |  *  *  * 40  *  *  *  *  *  * | 0  2  0  0 0
oo3ox .. *b3xo ..&#x   4  6 |   6  12  12 |   4  0  12   6   4   0   4 |  1  0  0   4   0   4  0  0  1  0  0 |  *  *  *  * 80  *  *  *  *  * | 0  1  1  0 0
.. ox3oo *b3xo ..&#x   4  6 |   6  12  12 |   4  0  12   6   0   4   4 |  0  1  0   0   4   4  0  0  0  1  0 |  *  *  *  *  * 80  *  *  *  * | 0  1  0  1 0
.. ox .. *b3xo3oo&#x   6  4 |  12  12   6 |   4  4   6  12   0   0   4 |  0  0  1   0   0   4  4  0  0  0  1 |  *  *  *  *  *  * 80  *  *  * | 0  0  1  1 0
.o3.x3.o *b3.o ..      0 24 |   0   0  96 |   0  0   0   0  32  32  32 |  0  0  0   0   0   0  0  8  8  8  0 |  *  *  *  *  *  *  * 10  *  * | 0  1  0  0 1
.o3.x .. *b3.o3.o      0 10 |   0   0  30 |   0  0   0   0  10   0  20 |  0  0  0   0   0   0  0  0  5  0  5 |  *  *  *  *  *  *  *  * 16  * | 0  0  1  0 1
.. .x3.o *b3.o3.o      0 10 |   0   0  30 |   0  0   0   0   0  10  20 |  0  0  0   0   0   0  0  0  0  5  5 |  *  *  *  *  *  *  *  *  * 16 | 0  0  0  1 1
---------------------+-------+-------------+----------------------------+-------------------------------------+-------------------------------+-------------
o.3o.3o. *b3x.3o.     40  0 | 240   0   0 | 320 80   0   0   0   0   0 | 80 80 80   0   0   0  0  0  0  0  0 | 10 16 16  0  0  0  0  0  0  0 | 1  *  *  * *
oo3ox3oo *b3xo ..&#x   8 24 |  24  48  96 |  32  0  96  24  32  32  32 |  8  8  0  32  32  32  0  8  8  8  0 |  1  0  0  8  8  8  0  1  0  0 | * 10  *  * *
oo3ox .. *b3xo3oo&#x  10 10 |  30  30  30 |  20 10  30  30  10   0  20 |  5  0  5  10   0  20 10  0  5  0  5 |  0  1  0  0  5  0  5  0  1  0 | *  * 16  * *
.. ox3oo *b3xo3oo&#x  10 10 |  30  30  30 |  20 10  30  30   0  10  20 |  0  5  5   0  10  20 10  0  0  5  5 |  0  0  1  0  0  5  5  0  0  1 | *  *  * 16 *
.o3.x3.o *b3.o3.o      0 80 |   0   0 480 |   0  0   0   0 160 160 320 |  0  0  0   0   0   0  0 40 80 80 80 |  0  0  0  0  0  0  0 10 16 16 | *  *  *  * 1

© 2004-2019
top of page