Acronym pabac span
Name partially bicontracted small prismated penteract
Circumradius ...
Lace city
in approx. ASCII-art
 line   esquidpy     esquidpy  line 		-- quawros
                                    
                                    
                                    
                                    
esquidpy pexco        pexco esquidpy		-- bicyte ausodip
                                    
                                    
                                    
                                    
                                    
                                    
esquidpy pexco        pexco esquidpy		-- bicyte ausodip
                                    
                                    
                                    
                                    
 line   esquidpy     esquidpy  line 		-- quawros
square   squobcu  square 		-- quawros
                         
                         
                         
                         
squobcu  pactic   squobcu		-- bicyte ausodip
                         
                         
                         
                         
                         
                         
squobcu  pactic   squobcu		-- bicyte ausodip
                         
                         
                         
                         
square   squobcu  square 		-- quawros

  |        |        +-- pacsid pith
  |        +----------- pacsrit
  +-------------------- pacsid pith
o3o4x    x3o4x    o3o4x		-- pacsid pith
                       
                       
                       
                       
x3o4x    o3x4x    x3o4x		-- pacsrit
                       
                       
                       
                       
o3o4x    x3o4x    o3o4x		-- pacsid pith
Coordinates
  • (0, 0; 1/2, (1+sqrt(2))/2, (1+sqrt(2))/2)   & all permutations within last 3 coords, all changes of sign
  • (1/sqrt(2), 0; 1/2, 1/2, (1+sqrt(2))/2)     & all permutations within each subset, all changes of sign
  • (1/sqrt(2), 1/sqrt(2); 1/2, 1/2, 1/2)       & all changes of sign
Confer
uniform relative:
rat   span  
general polytopal classes:
partial Stott expansions  

This CRF polyteron can be obtained from span by partial Stott contracting only within 2 perpendicular axial directions.


Incidence matrix according to Dynkin symbol

qoo4oxo oxo3oox4xxx&#zxt   → both heights = 0

o..4o.. o..3o..4o..     | 32  *  * |  3   6  0  0  0   0  0  0 |  3  3   6  12  0  0  0  0   0  0  0  0 0 | 1  3  6  2  6  6  0  0  0  0  0 | 2  1  3  3 0
.o.4.o. .o.3.o.4.o.     |  * 96  * |  0   2  2  2  2   2  0  0 |  0  2   4   4  4  1  2  1   4  2  1  2 0 | 0  4  4  2  4  2  2  2  4  1  2 | 1  2  4  2 1
..o4..o ..o3..o4..o     |  *  * 24 |  0   0  0  0  0   8  2  1 |  0  0   0   0  0  0  0  0   8  4  8  8 1 | 0  4  0  0  0  0  0  8  8  4  4 | 0  4  4  0 2
------------------------+----------+---------------------------+------------------------------------------+---------------------------------+-------------
... ... ... ... x..     |  2  0  0 | 48   *  *  *  *   *  *  * |  2  0   0   4  0  0  0  0   0  0  0  0 0 | 1  0  2  0  2  4  0  0  0  0  0 | 2  0  1  2 0
oo.4oo. oo.3oo.4oo.&#x  |  1  1  0 |  * 192  *  *  *   *  *  * |  0  1   2   2  0  0  0  0   0  0  0  0 0 | 0  2  2  1  2  1  0  0  0  0  0 | 1  1  2  1 0
... .x. ... ... ...     |  0  2  0 |  *   * 96  *  *   *  *  * |  0  1   0   0  2  0  0  0   2  0  0  0 0 | 0  2  2  0  0  0  1  1  2  0  0 | 0  1  2  1 1
... ... .x. ... ...     |  0  2  0 |  *   *  * 96  *   *  *  * |  0  0   2   0  0  1  1  0   0  1  0  0 0 | 0  2  0  2  2  0  0  0  0  1  1 | 1  2  2  0 0
... ... ... ... .x.     |  0  2  0 |  *   *  *  * 96   *  *  * |  0  0   0   2  2  0  1  1   0  0  0  1 0 | 0  0  2  0  2  2  2  0  2  0  1 | 1  0  2  2 1
.oo4.oo .oo3.oo4.oo&#x  |  0  1  1 |  *   *  *  *  * 192  *  * |  0  0   0   0  0  0  0  0   2  1  1  1 0 | 0  2  0  0  0  0  0  2  2  1  1 | 0  2  2  0 1
... ... ... ..x ...     |  0  0  2 |  *   *  *  *  *   * 24  * |  0  0   0   0  0  0  0  0   0  0  4  0 1 | 0  0  0  0  0  0  0  4  0  4  0 | 0  4  0  0 1
... ... ... ... ..x     |  0  0  2 |  *   *  *  *  *   *  * 12 |  0  0   0   0  0  0  0  0   0  0  0  8 0 | 0  0  0  0  0  0  0  0  8  0  4 | 0  0  4  0 2
------------------------+----------+---------------------------+------------------------------------------+---------------------------------+-------------
... ... ... o..4x..     |  4  0  0 |  4   0  0  0  0   0  0  0 | 24  *   *   *  *  *  *  *   *  *  *  * * | 1  0  0  0  0  2  0  0  0  0  0 | 2  0  0  1 0
... ox. ... ... ...&#x  |  1  2  0 |  0   2  1  0  0   0  0  0 |  * 96   *   *  *  *  *  *   *  *  *  * * | 0  2  2  0  0  0  0  0  0  0  0 | 0  1  2  1 0
... ... ox. ... ...&#x  |  1  2  0 |  0   2  0  1  0   0  0  0 |  *  * 192   *  *  *  *  *   *  *  *  * * | 0  1  0  1  1  0  0  0  0  0  0 | 1  1  1  0 0
... ... ... ... xx.&#x  |  2  2  0 |  1   2  0  0  1   0  0  0 |  *  *   * 192  *  *  *  *   *  *  *  * * | 0  0  1  0  1  1  0  0  0  0  0 | 1  0  1  1 0
... .x. ... ... .x.     |  0  4  0 |  0   0  2  0  2   0  0  0 |  *  *   *   * 96  *  *  *   *  *  *  * * | 0  0  1  0  0  0  1  0  1  0  0 | 0  0  1  1 1
... ... .x.3.o. ...     |  0  3  0 |  0   0  0  3  0   0  0  0 |  *  *   *   *  * 32  *  *   *  *  *  * * | 0  0  0  2  0  0  0  0  0  1  0 | 1  2  0  0 0
... ... .x. ... .x.     |  0  4  0 |  0   0  0  2  2   0  0  0 |  *  *   *   *  *  * 48  *   *  *  *  * * | 0  0  0  0  2  0  0  0  0  0  1 | 1  0  2  0 0
... ... ... .o.4.x.     |  0  4  0 |  0   0  0  0  4   0  0  0 |  *  *   *   *  *  *  * 24   *  *  *  * * | 0  0  0  0  0  2  2  0  0  0  0 | 1  0  0  2 1
... .xo ... ... ...&#x  |  0  2  1 |  0   0  1  0  0   2  0  0 |  *  *   *   *  *  *  *  * 192  *  *  * * | 0  1  0  0  0  0  0  1  1  0  0 | 0  1  1  0 1
... ... .xo ... ...&#x  |  0  2  1 |  0   0  0  1  0   2  0  0 |  *  *   *   *  *  *  *  *   * 96  *  * * | 0  2  0  0  0  0  0  0  0  1  1 | 0  2  2  0 0
... ... ... .ox ...&#x  |  0  1  2 |  0   0  0  0  0   2  1  0 |  *  *   *   *  *  *  *  *   *  * 96  * * | 0  0  0  0  0  0  0  2  0  1  0 | 0  2  0  0 1
... ... ... ... .xx&#x  |  0  2  2 |  0   0  0  0  1   2  0  1 |  *  *   *   *  *  *  *  *   *  *  * 96 * | 0  0  0  0  0  0  0  0  2  0  1 | 0  0  2  0 1
... ... ..o3..x ...     |  0  0  3 |  0   0  0  0  0   0  3  0 |  *  *   *   *  *  *  *  *   *  *  *  * 8 | 0  0  0  0  0  0  0  0  0  4  0 | 0  4  0  0 0
------------------------+----------+---------------------------+------------------------------------------+---------------------------------+-------------
... ... o..3o..4x..       8  0  0 | 12   0  0  0  0   0  0  0 |  6  0   0   0  0  0  0  0   0  0  0  0 0 | 4  *  *  *  *  *  *  *  *  *  * | 2  0  0  0 0
... oxo oxo ... ...&#xt   1  4  1 |  0   4  2  2  0   4  0  0 |  0  2   2   0  0  0  0  0   2  2  0  0 0 | * 96  *  *  *  *  *  *  *  *  * | 0  1  1  0 0
... ox. ... ... xx.&#x    2  4  0 |  1   4  2  0  2   0  0  0 |  0  2   0   2  1  0  0  0   0  0  0  0 0 | *  * 96  *  *  *  *  *  *  *  * | 0  0  1  1 0
... ... ox.3oo. ...&#x    1  3  0 |  0   3  0  3  0   0  0  0 |  0  0   3   0  0  1  0  0   0  0  0  0 0 | *  *  * 64  *  *  *  *  *  *  * | 1  1  0  0 0
... ... ox. ... xx.&#x    2  4  0 |  1   4  0  2  2   0  0  0 |  0  0   2   2  0  0  1  0   0  0  0  0 0 | *  *  *  * 96  *  *  *  *  *  * | 1  0  1  0 0
... ... ... oo.4xx.&#x    4  4  0 |  4   4  0  0  4   0  0  0 |  1  0   0   4  0  0  0  1   0  0  0  0 0 | *  *  *  *  * 48  *  *  *  *  * | 1  0  0  1 0
... .x. ... .o.4.x.       0  8  0 |  0   0  4  0  8   0  0  0 |  0  0   0   0  4  0  0  2   0  0  0  0 0 | *  *  *  *  *  * 24  *  *  *  * | 0  0  0  1 1
... .xo ... .ox ...&#x    0  2  2 |  0   0  1  0  0   4  1  0 |  0  0   0   0  0  0  0  0   2  0  2  0 0 | *  *  *  *  *  *  * 96  *  *  * | 0  1  0  0 1
... .xo ... ... .xx&#x    0  4  2 |  0   0  2  0  2   4  0  1 |  0  0   0   0  1  0  0  0   2  0  0  2 0 | *  *  *  *  *  *  *  * 96  *  * | 0  0  1  0 1
... ... .xo3.ox ...&#x    0  3  3 |  0   0  0  3  0   6  3  0 |  0  0   0   0  0  1  0  0   0  3  3  0 1 | *  *  *  *  *  *  *  *  * 32  * | 0  2  0  0 0
... ... .xo ... .xx&#x    0  4  2 |  0   0  0  2  2   4  0  1 |  0  0   0   0  0  0  1  0   0  2  0  2 0 | *  *  *  *  *  *  *  *  *  * 48 | 0  0  2  0 0
------------------------+----------+---------------------------+------------------------------------------+---------------------------------+-------------
qo. ... ox.3oo.4xx.&#zx  16 24  0 | 24  48  0 24 24   0  0  0 | 12  0  48  48  0  8 12  6   0  0  0  0 0 | 2  0  0 16 24 12  0  0  0  0  0 | 4  *  *  * *
... oxo oxo3oox ...&#xt   1  6  3 |  0   6  3  6  0  12  3  0 |  0  3   6   0  0  2  0  0   6  6  6  0 1 | 0  3  0  2  0  0  0  3  0  2  0 | * 32  *  * *
... oxo oxo ... xxx&#xt   2  8  2 |  1   8  4  4  4   8  0  1 |  0  4   4   4  2  0  2  0   4  4  0  4 0 | 0  2  2  0  2  0  0  0  2  0  2 | *  * 48  * *
... ox. ... oo.4xx.&#x    4  8  0 |  4   8  4  0  8   0  0  0 |  1  4   0   8  4  0  0  2   0  0  0  0 0 | 0  0  4  0  0  2  1  0  0  0  0 | *  *  * 24 *
.oo4.xo ... .ox4.xx&#zx   0 16  8 |  0   0 16  0 16  32  4  4 |  0  0   0   0 16  0  0  4  32  0 16 16 0 | 0  0  0  0  0  0  4 16 16  0  0 | *  *  *  * 6

© 2004-2022
top of page