Acronym gyprip
Name gyrated prip
Circumradius sqrt(13/5) = 1.612452
Lace city
in approx. ASCII-art 
    o3x  x3x  x3o  		-- x3o3x (co)
                   
o3x       u3x  u3o 		-- u3o3x ((u,x)-co)
                   
 x3x  u3x  x3u  x3x		-- x3x3x (toe)
                   
     x3x  o3u  o3x 		-- o3x3x (inv. tut)
Dihedral angles
  • at {6} between hip and tricu:   arccos(-sqrt[27/32]) = 156.716268°
  • at {6} between tricu and tut:   arccos(-7/8) = 151.044976°
  • at {4} between hip and trip:   arccos(-2/3) = 131.810315°
  • at {3} between co and trip:   arccos[-sqrt(3/8)] = 127.761244°
  • at {6} between hip and tut:   arccos[-sqrt(3/8)] = 127.761244°
  • at {3} between tricu and trip:   arccos[-sqrt(3/8)] = 127.761244°
  • at {4} between co and hip:   arccos[-1/sqrt(6)] = 114.094843°
  • at {4} between hip and tricu:   arccos[-1/sqrt(6)] = 114.094843°
  • at {3} between co and tut:   arccos(-1/4) = 104.477512°
  • at {3} between tricu and tut:   arccos(-1/4) = 104.477512°
Face vector 60, 150, 124, 34
Confer
uniform relative:
prip  
segmentochora:
tut || toe  
related CRFs:
co || (u,c)-co || toe   autpen  

This polychoron is obtained from prip by dissection along its pseudo toe layer and then re-glueing those parts with interchanged roles of the hexagons. This dissects also the there located coes into pairs of tricues. Obviously this operation does not change its overall orbiformity. This is a rare case of true 4D gyration!

The Stott contraction of this polychoron is autpen.


Incidence matrix according to Dynkin symbol

xuxo3ooxx3xxxx&#xt   → all heights = sqrt(5/8) = 0.790569
(co || pseudo (u,x)-co || pseudo toe || inv. tut)

o...3o...3o...     | 12  *  *  * |  2  2  1  0  0  0  0  0  0  0 0 | 1 2 1  2  2 0  0  0 0 0 0  0  0  0 0 0 | 1 1 2 1 0 0 0 0 0
.o..3.o..3.o..     |  * 12  *  * |  0  0  1  2  2  0  0  0  0  0 0 | 0 0 0  2  2 1  1  2 0 0 0  0  0  0 0 0 | 0 1 2 1 1 0 0 0 0
..o.3..o.3..o.     |  *  * 24  * |  0  0  0  0  1  1  1  1  1  0 0 | 0 0 0  1  0 0  1  1 1 1 1  1  1  1 0 0 | 0 1 1 0 1 1 1 1 0
...o3...o3...o     |  *  *  * 12 |  0  0  0  0  0  0  0  0  2  2 1 | 0 0 0  0  0 0  0  0 0 0 0  1  2  2 1 2 | 0 0 0 0 0 1 1 2 1
-------------------+-------------+---------------------------------+----------------------------------------+------------------
x... .... ....     |  2  0  0  0 | 12  *  *  *  *  *  *  *  *  * * | 1 1 0  1  0 0  0  0 0 0 0  0  0  0 0 0 | 1 1 1 0 0 0 0 0 0
.... .... x...     |  2  0  0  0 |  * 12  *  *  *  *  *  *  *  * * | 0 1 1  0  1 0  0  0 0 0 0  0  0  0 0 0 | 1 0 1 1 0 0 0 0 0
oo..3oo..3oo..&#x  |  1  1  0  0 |  *  * 12  *  *  *  *  *  *  * * | 0 0 0  2  2 0  0  0 0 0 0  0  0  0 0 0 | 0 1 2 1 0 0 0 0 0
.... .... .x..     |  0  2  0  0 |  *  *  * 12  *  *  *  *  *  * * | 0 0 0  0  1 1  0  1 0 0 0  0  0  0 0 0 | 0 0 1 1 1 0 0 0 0
.oo.3.oo.3.oo.&#x  |  0  1  1  0 |  *  *  *  * 24  *  *  *  *  * * | 0 0 0  1  0 0  1  1 0 0 0  0  0  0 0 0 | 0 1 1 0 1 0 0 0 0
..x. .... ....     |  0  0  2  0 |  *  *  *  *  * 12  *  *  *  * * | 0 0 0  1  0 0  0  0 1 1 0  1  0  0 0 0 | 0 1 1 0 0 1 1 0 0
.... ..x. ....     |  0  0  2  0 |  *  *  *  *  *  * 12  *  *  * * | 0 0 0  0  0 0  1  0 1 0 1  0  1  0 0 0 | 0 1 0 0 1 1 0 1 0
.... .... ..x.     |  0  0  2  0 |  *  *  *  *  *  *  * 12  *  * * | 0 0 0  0  0 0  0  1 0 1 1  0  0  1 0 0 | 0 0 1 0 1 0 1 1 0
..oo3..oo3..oo&#x  |  0  0  1  1 |  *  *  *  *  *  *  *  * 24  * * | 0 0 0  0  0 0  0  0 0 0 0  1  1  1 0 0 | 0 0 0 0 0 1 1 1 0
.... ...x ....     |  0  0  0  2 |  *  *  *  *  *  *  *  *  * 12 * | 0 0 0  0  0 0  0  0 0 0 0  0  1  0 1 1 | 0 0 0 0 0 1 0 1 1
.... .... ...x     |  0  0  0  2 |  *  *  *  *  *  *  *  *  *  * 6 | 0 0 0  0  0 0  0  0 0 0 0  0  0  2 0 2 | 0 0 0 0 0 0 1 2 1
-------------------+-------------+---------------------------------+----------------------------------------+------------------
x...3o... ....     |  3  0  0  0 |  3  0  0  0  0  0  0  0  0  0 0 | 4 * *  *  * *  *  * * * *  *  *  * * * | 1 1 0 0 0 0 0 0 0
x... .... x...     |  4  0  0  0 |  2  2  0  0  0  0  0  0  0  0 0 | * 6 *  *  * *  *  * * * *  *  *  * * * | 1 0 1 0 0 0 0 0 0
.... o...3x...     |  3  0  0  0 |  0  3  0  0  0  0  0  0  0  0 0 | * * 4  *  * *  *  * * * *  *  *  * * * | 1 0 0 1 0 0 0 0 0
xux. .... ....&#xt |  2  2  2  0 |  1  0  2  0  2  1  0  0  0  0 0 | * * * 12  * *  *  * * * *  *  *  * * * | 0 1 1 0 0 0 0 0 0
.... .... xx..&#x  |  2  2  0  0 |  0  1  2  1  0  0  0  0  0  0 0 | * * *  * 12 *  *  * * * *  *  *  * * * | 0 0 1 1 0 0 0 0 0
.... .o..3.x..     |  0  3  0  0 |  0  0  0  3  0  0  0  0  0  0 0 | * * *  *  * 4  *  * * * *  *  *  * * * | 0 0 0 1 1 0 0 0 0
.... .ox. ....&#x  |  0  1  2  0 |  0  0  0  0  2  0  1  0  0  0 0 | * * *  *  * * 12  * * * *  *  *  * * * | 0 1 0 0 1 0 0 0 0
.... .... .xx.&#x  |  0  2  2  0 |  0  0  0  1  2  0  0  1  0  0 0 | * * *  *  * *  * 12 * * *  *  *  * * * | 0 0 1 0 1 0 0 0 0
..x.3..x. ....     |  0  0  6  0 |  0  0  0  0  0  3  3  0  0  0 0 | * * *  *  * *  *  * 4 * *  *  *  * * * | 0 1 0 0 0 1 0 0 0
..x. .... ..x.     |  0  0  4  0 |  0  0  0  0  0  2  0  2  0  0 0 | * * *  *  * *  *  * * 6 *  *  *  * * * | 0 0 1 0 0 0 1 0 0
.... ..x.3..x.     |  0  0  6  0 |  0  0  0  0  0  0  3  3  0  0 0 | * * *  *  * *  *  * * * 4  *  *  * * * | 0 0 0 0 1 0 0 1 0
..xo .... ....&#x  |  0  0  2  1 |  0  0  0  0  0  1  0  0  2  0 0 | * * *  *  * *  *  * * * * 12  *  * * * | 0 0 0 0 0 1 1 0 0
.... ..xx ....&#x  |  0  0  2  2 |  0  0  0  0  0  0  1  0  2  1 0 | * * *  *  * *  *  * * * *  * 12  * * * | 0 0 0 0 0 1 0 1 0
.... .... ..xx&#x  |  0  0  2  2 |  0  0  0  0  0  0  0  1  2  0 1 | * * *  *  * *  *  * * * *  *  * 12 * * | 0 0 0 0 0 0 1 1 0
...o3...x ....     |  0  0  0  3 |  0  0  0  0  0  0  0  0  0  3 0 | * * *  *  * *  *  * * * *  *  *  * 4 * | 0 0 0 0 0 1 0 0 1
.... ...x3...x     |  0  0  0  6 |  0  0  0  0  0  0  0  0  0  3 3 | * * *  *  * *  *  * * * *  *  *  * * 4 | 0 0 0 0 0 0 0 1 1
-------------------+-------------+---------------------------------+----------------------------------------+------------------
x...3o...3x...     ♦ 12  0  0  0 | 12 12  0  0  0  0  0  0  0  0 0 | 4 6 4  0  0 0  0  0 0 0 0  0  0  0 0 0 | 1 * * * * * * * *
xux.3oox. ....&#xt ♦  3  3  6  0 |  3  0  3  0  6  3  3  0  0  0 0 | 1 0 0  3  0 0  3  0 1 0 0  0  0  0 0 0 | * 4 * * * * * * *
xux. .... xxx.&#xt ♦  4  4  4  0 |  2  2  4  2  4  2  0  2  0  0 0 | 0 1 0  2  2 0  0  2 0 1 0  0  0  0 0 0 | * * 6 * * * * * *
.... oo..3xx..&#x  ♦  3  3  0  0 |  0  3  3  3  0  0  0  0  0  0 0 | 0 0 1  0  3 1  0  0 0 0 0  0  0  0 0 0 | * * * 4 * * * * *
.... .ox.3.xx.&#x  ♦  0  3  6  0 |  0  0  0  3  6  0  3  3  0  0 0 | 0 0 0  0  0 1  3  3 0 0 1  0  0  0 0 0 | * * * * 4 * * * *
..xo3..xx ....&#x  ♦  0  0  6  3 |  0  0  0  0  0  3  3  0  6  3 0 | 0 0 0  0  0 0  0  0 1 0 0  3  3  0 1 0 | * * * * * 4 * * *
..xo .... ..xx&#x  ♦  0  0  4  2 |  0  0  0  0  0  2  0  2  4  0 1 | 0 0 0  0  0 0  0  0 0 1 0  2  0  2 0 0 | * * * * * * 6 * *
.... ..xx3..xx&#x  ♦  0  0  6  6 |  0  0  0  0  0  0  3  3  6  3 3 | 0 0 0  0  0 0  0  0 0 0 1  0  3  3 0 1 | * * * * * * * 4 *
...o3...x3...x     ♦  0  0  0 12 |  0  0  0  0  0  0  0  0  0 12 6 | 0 0 0  0  0 0  0  0 0 0 0  0  0  0 4 4 | * * * * * * * * 1

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