Acronym grip
Name great rhombated pentachoron,
cantitruncated pentachoron
 
 ©
Cross sections
 ©
Circumradius sqrt(17/5) = 1.843909
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o3o o3o3o . o3o . o o . o3o . o3o3o
1x3x3x3o x3x3x .
toe first
x3x . o
{6} first
x . x3o
trip first
. x3x3o
tut first
2 x3u3o . u3x . x u . u3o . u3x3o
3a u3x3o . x3u . u x . H3o . x3u3o
3b H . x3x
4a x3x3o .
opposite tut
o3H . x u . u3x . x3x3x
opposite toe
4b x3x . H
5   o3u . u x . x3u  
6 o3x . x
opposite trip
o . x3x
opposite {6}
(H=hh=x+u)
Lace city
in approx. ASCII-art
   x3x  u3o  x3o    		-- x3x3o (tut)
                    
  u3x  H3o       x3o		-- u3x3o ((u,x)-tut)
                    
 x3u       H3o  u3o 		-- x3u3o ((x,u)-tut)
                    
x3x  x3u  u3x  x3x  		-- x3x3x (toe)
      x o   u x   x u   o x      		-- x3x3o (tut)
                                 
                                 
   u o   w x         x w   o u   		-- u3x3o ((u,x)-tut)
                                 
                                 
x o         w u   u w         o x		-- x3u3o ((x,u)-tut)
                                 
                                 
   x x   u u  xw wx  u u   x x   		-- x3x3x (toe)
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: toe trip tut
grip 5105
)
Dihedral angles
  • at {3} between trip and tut:   arccos(-sqrt[3/8]) = 127.761244°
  • at {4} between toe and trip:   arccos(-sqrt[1/6]) = 114.094843°
  • at {6} between toe and tut:   arccos(-1/4) = 104.477512°
  • at {6} between toe and toe:   arccos(1/4) = 75.522488°
Confer
Grünbaumian relatives:
2grip  
related CRFs:
tutatoe augrip  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

Note that grip can be thought of as the external blend of 1 srip + 5 coatuts + 10 trafs + 10 tricufs + 5 oct || toe. This decomposition is described as the (also subdimensioanlly) degenerate segmentoteron xo3ox3xx3ox&#x.


Incidence matrix according to Dynkin symbol

x3x3x3o

. . . . | 60 |  1  1  2 |  1  2  2  1 | 2  1 1
--------+----+----------+-------------+-------
x . . . |  2 | 30  *  * |  1  2  0  0 | 2  1 0
. x . . |  2 |  * 30  * |  1  0  2  0 | 2  0 1
. . x . |  2 |  *  * 60 |  0  1  1  1 | 1  1 1
--------+----+----------+-------------+-------
x3x . . |  6 |  3  3  0 | 10  *  *  * | 2  0 0
x . x . |  4 |  2  0  2 |  * 30  *  * | 1  1 0
. x3x . |  6 |  0  3  3 |  *  * 20  * | 1  0 1
. . x3o |  3 |  0  0  3 |  *  *  * 20 | 0  1 1
--------+----+----------+-------------+-------
x3x3x .  24 | 12 12 12 |  4  6  4  0 | 5  * *
x . x3o   6 |  3  0  6 |  0  3  0  2 | * 10 *
. x3x3o  12 |  0  6 12 |  0  0  4  4 | *  * 5

snubbed forms: β3x3x3o, x3β3x3o, x3x3β3o, β3β3x3o, β3x3β3o, x3β3β3o, β3β3β3o

x3x3x3/2o

. . .   . | 60 |  1  1  2 |  1  2  2  1 | 2  1 1
----------+----+----------+-------------+-------
x . .   . |  2 | 30  *  * |  1  2  0  0 | 2  1 0
. x .   . |  2 |  * 30  * |  1  0  2  0 | 2  0 1
. . x   . |  2 |  *  * 60 |  0  1  1  1 | 1  1 1
----------+----+----------+-------------+-------
x3x .   . |  6 |  3  3  0 | 10  *  *  * | 2  0 0
x . x   . |  4 |  2  0  2 |  * 30  *  * | 1  1 0
. x3x   . |  6 |  0  3  3 |  *  * 20  * | 1  0 1
. . x3/2o |  3 |  0  0  3 |  *  *  * 20 | 0  1 1
----------+----+----------+-------------+-------
x3x3x   .  24 | 12 12 12 |  4  6  4  0 | 5  * *
x . x3/2o   6 |  3  0  6 |  0  3  0  2 | * 10 *
. x3x3/2o  12 |  0  6 12 |  0  0  4  4 | *  * 5

xuxx3xxux3ooox&#xt   → all heights = sqrt(5/8) = 0.790569
(tut || pseudo (u,x)-tut || pseudo (x,u)-tut || toe)

o...3o...3o...     | 12  *  *  * | 1  2  1  0  0 0  0  0  0  0 | 2 1  2 1 0  0  0  0 0 0 0 | 1 1 2 0 0 0
.o..3.o..3.o..     |  * 12  *  * | 0  0  1  2  1 0  0  0  0  0 | 0 0  2 1 1  2  0  0 0 0 0 | 0 1 2 1 0 0
..o.3..o.3..o.     |  *  * 12  * | 0  0  0  0  1 1  2  0  0  0 | 0 0  0 1 0  2  2  1 0 0 0 | 0 0 2 1 1 0
...o3...o3...o     |  *  *  * 24 | 0  0  0  0  0 0  1  1  1  1 | 0 0  0 0 0  1  1  1 1 1 1 | 0 0 1 1 1 1
-------------------+-------------+-----------------------------+---------------------------+------------
x... .... ....     |  2  0  0  0 | 6  *  *  *  * *  *  *  *  * | 2 0  0 1 0  0  0  0 0 0 0 | 1 0 2 0 0 0
.... x... ....     |  2  0  0  0 | * 12  *  *  * *  *  *  *  * | 1 1  1 0 0  0  0  0 0 0 0 | 1 1 1 0 0 0
oo..3oo..3oo..&#x  |  1  1  0  0 | *  * 12  *  * *  *  *  *  * | 0 0  2 1 0  0  0  0 0 0 0 | 0 1 2 0 0 0
.... .x.. ....     |  0  2  0  0 | *  *  * 12  * *  *  *  *  * | 0 0  1 0 1  1  0  0 0 0 0 | 0 1 1 1 0 0
.oo.3.oo.3.oo.&#x  |  0  1  1  0 | *  *  *  * 12 *  *  *  *  * | 0 0  0 1 0  2  0  0 0 0 0 | 0 0 2 1 0 0
..x. .... ....     |  0  0  2  0 | *  *  *  *  * 6  *  *  *  * | 0 0  0 1 0  0  2  0 0 0 0 | 0 0 2 0 1 0
..oo3..oo3..oo&#x  |  0  0  1  1 | *  *  *  *  * * 24  *  *  * | 0 0  0 0 0  1  1  1 0 0 0 | 0 0 1 1 1 0
...x .... ....     |  0  0  0  2 | *  *  *  *  * *  * 12  *  * | 0 0  0 0 0  0  1  0 1 1 0 | 0 0 1 0 1 1
.... ...x ....     |  0  0  0  2 | *  *  *  *  * *  *  * 12  * | 0 0  0 0 0  1  0  0 1 0 1 | 0 0 1 1 0 1
.... .... ...x     |  0  0  0  2 | *  *  *  *  * *  *  *  * 12 | 0 0  0 0 0  0  0  1 0 1 1 | 0 0 0 1 1 1
-------------------+-------------+-----------------------------+---------------------------+------------
x...3x... ....     |  6  0  0  0 | 3  3  0  0  0 0  0  0  0  0 | 4 *  * * *  *  *  * * * * | 1 0 1 0 0 0
.... x...3o...     |  3  0  0  0 | 0  3  0  0  0 0  0  0  0  0 | * 4  * * *  *  *  * * * * | 1 1 0 0 0 0
.... xx.. ....&#x  |  2  2  0  0 | 0  1  2  1  0 0  0  0  0  0 | * * 12 * *  *  *  * * * * | 0 1 1 0 0 0
xux. .... ....&#xt |  2  2  2  0 | 1  0  2  0  2 1  0  0  0  0 | * *  * 6 *  *  *  * * * * | 0 0 2 0 0 0
.... .x..3.o..     |  0  3  0  0 | 0  0  0  3  0 0  0  0  0  0 | * *  * * 4  *  *  * * * * | 0 1 0 1 0 0
.... .xux ....&#xt |  0  2  2  2 | 0  0  0  1  2 0  2  0  1  0 | * *  * * * 12  *  * * * * | 0 0 1 1 0 0
..xx .... ....&#x  |  0  0  2  2 | 0  0  0  0  0 1  2  1  0  0 | * *  * * *  * 12  * * * * | 0 0 1 0 1 0
.... .... ..ox&#x  |  0  0  1  2 | 0  0  0  0  0 0  2  0  0  1 | * *  * * *  *  * 12 * * * | 0 0 0 1 1 0
...x3...x ....     |  0  0  0  6 | 0  0  0  0  0 0  0  3  3  0 | * *  * * *  *  *  * 4 * * | 0 0 1 0 0 1
...x .... ...x     |  0  0  0  4 | 0  0  0  0  0 0  0  2  0  2 | * *  * * *  *  *  * * 6 * | 0 0 0 0 1 1
.... ...x3...x     |  0  0  0  6 | 0  0  0  0  0 0  0  0  3  3 | * *  * * *  *  *  * * * 4 | 0 0 0 1 0 1
-------------------+-------------+-----------------------------+---------------------------+------------
x...3x...3o...      12  0  0  0 | 6 12  0  0  0 0  0  0  0  0 | 4 4  0 0 0  0  0  0 0 0 0 | 1 * * * * *
.... xx..3oo..&#x    3  3  0  0 | 0  3  3  3  0 0  0  0  0  0 | 0 1  3 0 1  0  0  0 0 0 0 | * 4 * * * *
xuxx3xxux ....&#xt   6  6  6  6 | 3  3  6  3  6 3  6  3  3  0 | 1 0  3 3 0  3  3  0 1 0 0 | * * 4 * * *
.... .xux3.oox&#xt   0  3  3  6 | 0  0  0  3  3 0  6  0  3  3 | 0 0  0 0 1  3  0  3 0 0 1 | * * * 4 * *
..xx .... ..ox&#x    0  0  2  4 | 0  0  0  0  0 1  4  2  0  2 | 0 0  0 0 0  0  2  2 0 1 0 | * * * * 6 *
...x3...x3...x       0  0  0 24 | 0  0  0  0  0 0  0 12 12 12 | 0 0  0 0 0  0  0  0 4 6 4 | * * * * * 1

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