Acronym pac scant
Name partially contracted small cellated penteractitriacontiditeron
Circumradius ...
Lace city
in approx. ASCII-art
       square   square        	-- cube
                            
                            
                            
square squobcu  squobcu square	-- pacsid pith
                            
                            
                            
                            
                            
square squobcu  squobcu square	-- pacsid pith
                            
                            
                            
       square   square        	-- cube
       o3o4x       		-- cube
                   
                   
                   
o3o4x  x3o4x  o3o4x		-- pacsid pith
                   
                   
                   
                   
                   
o3o4x  x3o4x  o3o4x		-- pacsid pith
                   
                   
                   
       o3o4x       		-- cube

  |      |      +-- o3o3o4x (tes)
  |      +--------- x3o3o4x (sidpith)
  +---------------- o3o3o4x (tes)
Coordinates
  • (0; 1/2, 1/2, 1/2, (1+sqrt(2))/2)   & all permutations within all but first coord, all changes of sign
  • (1/sqrt(2); 1/2, 1/2, 1/2, 1/2)       & all changes of sign
Confer
uniform relative:
tac   scant   sidpithip  
general polytopal classes:
partial Stott expansions  

This CRF polyteron can be obtained from scant by partial Stott contracting only within axial direction, i.e. withdrawing the medial segment, the sidpithip, from scant.


Incidence matrix according to Dynkin symbol

qo ox3oo3oo4xx&#zx   → height = 0

o. o.3o.3o.4o.    | 32  * |  4   4  0  0 |  6   6  12  0  0  0 |  4   4  12 12  0  0  0 0 | 1  1  4  6  4
.o .o3.o3.o4.o    |  * 64 |  0   2  3  3 |  0   6   6  3  6  3 |  0   6  12  6  1  3  3 1 | 0  2  6  6  2
------------------+-------+--------------+---------------------+--------------------------+--------------
.. .. .. .. x.    |  2  0 | 64   *  *  * |  3   0   3  0  0  0 |  3   0   3  6  0  0  0 0 | 1  0  1  3  3
oo oo3oo3oo4oo&#x |  1  1 |  * 128  *  * |  0   3   3  0  0  0 |  0   3   6  3  0  0  0 0 | 0  1  3  3  1
.. .x .. .. ..    |  0  2 |  *   * 96  * |  0   2   0  2  2  0 |  0   4   4  0  1  2  1 0 | 0  2  4  2  0
.. .. .. .. .x    |  0  2 |  *   *  * 96 |  0   0   2  0  2  2 |  0   0   4  4  0  1  2 1 | 0  0  2  4  2
------------------+-------+--------------+---------------------+--------------------------+--------------
.. .. .. o.4x.    |  4  0 |  4   0  0  0 | 48   *   *  *  *  * |  2   0   0  2  0  0  0 0 | 1  0  0  1  2
.. ox .. .. ..&#x |  1  2 |  0   2  1  0 |  * 192   *  *  *  * |  0   2   2  0  0  0  0 0 | 0  1  2  1  0
.. .. .. .. xx&#x |  2  2 |  1   2  0  1 |  *   * 192  *  *  * |  0   0   2  2  0  0  0 0 | 0  0  1  2  1
.. .x3.o .. ..    |  0  3 |  0   0  3  0 |  *   *   * 64  *  * |  0   2   0  0  1  1  0 0 | 0  2  2  0  0
.. .x .. .. .x    |  0  4 |  0   0  2  2 |  *   *   *  * 96  * |  0   0   2  0  0  1  1 0 | 0  0  2  2  0
.. .. .. .o4.x    |  0  4 |  0   0  0  4 |  *   *   *  *  * 48 |  0   0   0  2  0  0  1 1 | 0  0  0  2  2
------------------+-------+--------------+---------------------+--------------------------+--------------
.. .. o.3o.4x.      8  0 | 12   0  0  0 |  6   0   0  0  0  0 | 16   *   *  *  *  *  * * | 1  0  0  0  1
.. ox3oo .. ..&#x   1  3 |  0   3  3  0 |  0   3   0  1  0  0 |  * 128   *  *  *  *  * * | 0  1  1  0  0
.. ox .. .. xx&#x   2  4 |  1   4  2  2 |  0   2   2  0  1  0 |  *   * 192  *  *  *  * * | 0  0  1  1  0
.. .. .. oo4xx&#x   4  4 |  4   4  0  4 |  1   0   4  0  0  1 |  *   *   * 96  *  *  * * | 0  0  0  1  1
.. .x3.o3.o ..      0  4 |  0   0  6  0 |  0   0   0  4  0  0 |  *   *   *  * 16  *  * * | 0  2  0  0  0
.. .x3.o .. .x      0  6 |  0   0  6  3 |  0   0   0  2  3  0 |  *   *   *  *  * 32  * * | 0  0  2  0  0
.. .x .. .o4.x      0  8 |  0   0  4  8 |  0   0   0  0  4  2 |  *   *   *  *  *  * 24 * | 0  0  0  2  0
.. .. .o3.o4.x      0  8 |  0   0  0 12 |  0   0   0  0  0  6 |  *   *   *  *  *  *  * 8 | 0  0  0  0  2
------------------+-------+--------------+---------------------+--------------------------+--------------
.. o.3o.3o.4x.     16  0 | 32   0  0  0 | 24   0   0  0  0  0 |  8   0   0  0  0  0  0 0 | 2  *  *  *  *
.. ox3oo3oo ..&#x   1  4 |  0   4  6  0 |  0   6   0  4  0  0 |  0   4   0  0  1  0  0 0 | * 32  *  *  *
.. ox3oo .. xx&#x   2  6 |  1   6  6  3 |  0   6   3  2  3  0 |  0   2   3  0  0  1  0 0 | *  * 64  *  *
.. ox .. oo4xx&#x   4  8 |  4   8  4  8 |  1   4   8  0  4  2 |  0   0   4  2  0  0  1 0 | *  *  * 48  *
.. .. oo3oo4xx&#x   8  8 | 12   8  0 12 |  6   0  12  0  0  6 |  1   0   0  6  0  0  0 1 | *  *  *  * 16

© 2004-2022
top of page