Acronym grit
Name great rhombated tesseract,
cantitruncated tesseract
    ©
Cross sections
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Circumradius sqrt[(11+5 sqrt(2))/2] = 3.005916
Vertex figure
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Vertex layers
LayerSymmetrySubsymmetries
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1o3x3x4x o3x3x .
tut first
o3x . x
trip first
o . x4x
{8} first
. x3x4x
girco first
2 o3x3w . o3u . w x . u4x . o3u4x
3 o3u3w . x3x . X u . x4w . o3x4w
4 o3U3x . o3U . w x . o4X . o3x4w
5a x3x3U . o3W . x U . x4w . o3u4x
5b x3w . X
6a x3w3u . x3W . x w . o4X . x3x4x
opposite girco
6b u3w . X W . u4x
7 u3w3x . u3U . w Y . x4x  
8a U3x3x . U3x . X w . o4X
8b W . u4x
9 x3U3o . x3U . X U . x4w
10 w3u3o . U3u . w x . o4X
11a w3x3o . W3x . x u . x4w
11b w3u . X
12a x3x3o .
opposite tut
W3o . x x . u4x
12b w3x . X
13   U3o . w o . x4x
opposite {8}
14 x3x . X  
15 u3o . w
16 x3o . x
opposite trip
(U=2x+q=u+q=x+w, X=x+2q=w+q), W=3x+q=u+w, Y=4x+q
Lace city
in approx. ASCII-art
 ©  
x4x u4x x4w   x4w u4x x4x
                         
u4x     o4X   o4X     u4x
                         
x4w o4X           o4X x4w
                         
                         
x4w o4X           o4X x4w
                         
u4x     o4X   o4X     u4x
                         
x4x u4x x4w   x4w u4x x4x
                    x3o            x3o                    
                                                          
          u3o                                u3o          
                                                          
x3x                                                    x3x
          U3o                                U3o          
                                                          
w3x                 W3o            W3o                 w3x
                                                          
                                                          
                                                          
w3u                 W3x            W3x                 w3u
                                                          
          U3u                                U3u          
x3U                                                    x3U
U3x                                                    U3x
          u3U                                u3U          
                                                          
u3w                 x3W            x3W                 u3w
                                                          
                                                          
                                                          
x3w                 o3W            o3W                 x3w
                                                          
          o3U                                o3U          
x3x                                                    x3x
                                                          
          o3u                                o3u          
                                                          
                    o3x            o3x                    
Coordinates ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: girco trip tut
grit 83216
)
Dihedral angles
  • at {3} between trip and tut:   150°
  • at {4} between girco and trip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {6} between girco and tut:   120°
  • at {8} between girco and girco:   90°
Confer
Grünbaumian relatives:
2grit  
decompositions:
tah || grit   tat || grit  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope grit is isomorphic to gaqrit, thereby replacing the octagons by octagrams, resp. replacing girco by quitco.

Note that grit can be thought of as the external blend of 1 tat + 16 tetatuts + 32 tepes + 8 ticagircoes. This decomposition is described as the degenerate segmentoteron oo3ox3xx4xx&#x. – Alternatively it can be decomposed into 1 tah + 16 tuttips + 32 triddips + 8 toagircoes according to oo3xx3xx4ox&#x. – Further, even so subdimensioanlly degenerate, grit can be decomposed into 1 prit + 16 tutcups + 32 tricupes + 24 squicufs + 8 sircoagircoes according to xo3xx3ox4xx&#x.


Incidence matrix according to Dynkin symbol

o3x3x4x

. . . . | 192 |   2  1  1 |  1  2  2  1 |  1  1 2
--------+-----+-----------+-------------+--------
. x . . |   2 | 192  *  * |  1  1  1  0 |  1  1 1
. . x . |   2 |   * 96  * |  0  2  0  1 |  1  0 2
. . . x |   2 |   *  * 96 |  0  0  2  1 |  0  1 2
--------+-----+-----------+-------------+--------
o3x . . |   3 |   3  0  0 | 64  *  *  * |  1  1 0
. x3x . |   6 |   3  3  0 |  * 64  *  * |  1  0 1
. x . x |   4 |   2  0  2 |  *  * 96  * |  0  1 1
. . x4x |   8 |   0  4  4 |  *  *  * 24 |  0  0 2
--------+-----+-----------+-------------+--------
o3x3x .   12 |  12  6  0 |  4  4  0  0 | 16  * *
o3x . x    6 |   6  0  3 |  2  0  3  0 |  * 32 *
. x3x4x   48 |  24 24 24 |  0  8 12  6 |  *  * 8

snubbed forms: o3β3x4x, o3x3β4x, o3x3x4s, o3β3β4x, o3β3x4β, o3x3β4β, o3β3β4β

o3/2x3x4x

.   . . . | 192 |   2  1  1 |  1  2  2  1 |  1  1 2
----------+-----+-----------+-------------+--------
.   x . . |   2 | 192  *  * |  1  1  1  0 |  1  1 1
.   . x . |   2 |   * 96  * |  0  2  0  1 |  1  0 2
.   . . x |   2 |   *  * 96 |  0  0  2  1 |  0  1 2
----------+-----+-----------+-------------+--------
o3/2x . . |   3 |   3  0  0 | 64  *  *  * |  1  1 0
.   x3x . |   6 |   3  3  0 |  * 64  *  * |  1  0 1
.   x . x |   4 |   2  0  2 |  *  * 96  * |  0  1 1
.   . x4x |   8 |   0  4  4 |  *  *  * 24 |  0  0 2
----------+-----+-----------+-------------+--------
o3/2x3x .   12 |  12  6  0 |  4  4  0  0 | 16  * *
o3/2x . x    6 |   6  0  3 |  2  0  3  0 |  * 32 *
.   x3x4x   48 |  24 24 24 |  0  8 12  6 |  *  * 8

xoooox3xuxxux4xxwwxx&#xt   → height(1,2) = height(2,3) = height(4,5) = height(5,6) = 1/sqrt(2) = 0.707107
                             height(3,4) = 1
(girco || pseudo (x,u)-tic || pseudo (w,x)-tic || pseudo (w,x)-tic || pseudo (x,u)-tic || girco)

o.....3o.....4o.....      & | 96  *  * |  1  1  1  1  0  0  0  0 |  1  1  1  1  1  1  0  0  0 | 1  1  1 1 0
.o....3.o....4.o....      & |  * 48  * |  0  0  0  2  1  1  0  0 |  0  0  0  1  2  2  1  0  0 | 0  1  1 2 0
..o...3..o...4..o...      & |  *  * 48 |  0  0  0  0  0  1  2  1 |  0  0  0  0  2  0  1  1  2 | 0  1  0 2 1
----------------------------+----------+-------------------------+----------------------------+------------
x..... ...... ......      & |  2  0  0 | 48  *  *  *  *  *  *  * |  1  1  0  1  0  0  0  0  0 | 1  1  1 0 0
...... x..... ......      & |  2  0  0 |  * 48  *  *  *  *  *  * |  1  0  1  0  1  0  0  0  0 | 1  1  0 1 0
...... ...... x.....      & |  2  0  0 |  *  * 48  *  *  *  *  * |  0  1  1  0  0  1  0  0  0 | 1  0  1 1 0
oo....3oo....4oo....&#x   & |  1  1  0 |  *  *  * 96  *  *  *  * |  0  0  0  1  1  1  0  0  0 | 0  1  1 1 0
...... ...... .x....      & |  0  2  0 |  *  *  *  * 24  *  *  * |  0  0  0  0  0  2  1  0  0 | 0  0  1 2 0
.oo...3.oo...4.oo...&#x   & |  0  1  1 |  *  *  *  *  * 48  *  * |  0  0  0  0  2  0  1  0  0 | 0  1  0 2 0
...... ..x... ......      & |  0  0  2 |  *  *  *  *  *  * 48  * |  0  0  0  0  1  0  0  1  1 | 0  1  0 1 1
..oo..3..oo..4..oo..&#x     |  0  0  2 |  *  *  *  *  *  *  * 24 |  0  0  0  0  0  0  1  0  2 | 0  0  0 2 1
----------------------------+----------+-------------------------+----------------------------+------------
x.....3x..... ......      & |  6  0  0 |  3  3  0  0  0  0  0  0 | 16  *  *  *  *  *  *  *  * | 1  1  0 0 0
x..... ...... x.....      & |  4  0  0 |  2  0  2  0  0  0  0  0 |  * 24  *  *  *  *  *  *  * | 1  0  1 0 0
...... x.....4x.....      & |  8  0  0 |  0  4  4  0  0  0  0  0 |  *  * 12  *  *  *  *  *  * | 1  0  0 1 0
xo.... ...... ......&#x   & |  2  1  0 |  1  0  0  2  0  0  0  0 |  *  *  * 48  *  *  *  *  * | 0  1  1 0 0
...... xux... ......&#xt  & |  2  2  2 |  0  1  0  2  0  2  1  0 |  *  *  *  * 48  *  *  *  * | 0  1  0 1 0
...... ...... xx....&#x   & |  2  2  0 |  0  0  1  2  1  0  0  0 |  *  *  *  *  * 48  *  *  * | 0  0  1 1 0
...... ...... .xwwx.&#xt    |  0  4  4 |  0  0  0  0  2  4  0  2 |  *  *  *  *  *  * 12  *  * | 0  0  0 2 0
..o...3..x... ......      & |  0  0  3 |  0  0  0  0  0  0  3  0 |  *  *  *  *  *  *  * 16  * | 0  1  0 0 1
...... ..xx.. ......&#x     |  0  0  4 |  0  0  0  0  0  0  2  2 |  *  *  *  *  *  *  *  * 24 | 0  0  0 1 1
----------------------------+----------+-------------------------+----------------------------+------------
x.....3x.....4x.....      &  48  0  0 | 24 24 24  0  0  0  0  0 |  8 12  6  0  0  0  0  0  0 | 2  *  * * *
xoo...3xux... ......&#xt  &   6  3  3 |  3  3  0  6  0  3  3  0 |  1  0  0  3  3  0  0  1  0 | * 16  * * *
xo.... ...... xx....&#x   &   4  2  0 |  2  0  2  4  1  0  0  0 |  0  1  0  2  0  2  0  0  0 | *  * 24 * *
...... xuxxux4xxwwxx&#xt     16 16 16 |  0  8  8 16  8 16  8  8 |  0  0  2  0  8  8  4  0  4 | *  *  * 6 *
..oo..3..xx.. ......&#x       0  0  6 |  0  0  0  0  0  0  6  3 |  0  0  0  0  0  0  0  2  3 | *  *  * * 8

wx3xx3xw *b3oo&#zx   → height = 0
(tegum sum of 2 mutually gyrated (w,x,x)-tahs)

o.3o.3o. *b3o.     | 96  * |  2  1  1  0  0 |  2  1  1  2  0  0 | 1 2  1 0
.o3.o3.o *b3.o     |  * 96 |  0  0  1  1  2 |  0  0  1  2  2  1 | 0 2  1 1
-------------------+-------+----------------+-------------------+---------
.. x. ..    ..     |  2  0 | 96  *  *  *  * |  1  1  0  1  0  0 | 1 1  1 0
.. .. x.    ..     |  2  0 |  * 48  *  *  * |  2  0  1  0  0  0 | 1 2  0 0
oo3oo3oo *b3oo&#x  |  1  1 |  *  * 96  *  * |  0  0  1  2  0  0 | 0 2  1 0
.x .. ..    ..     |  0  2 |  *  *  * 48  * |  0  0  1  0  2  0 | 0 2  0 1
.. .x ..    ..     |  0  2 |  *  *  *  * 96 |  0  0  0  1  1  1 | 0 1  1 1
-------------------+-------+----------------+-------------------+---------
.. x.3x.    ..     |  6  0 |  3  3  0  0  0 | 32  *  *  *  *  * | 1 1  0 0
.. x. .. *b3o.     |  3  0 |  3  0  0  0  0 |  * 32  *  *  *  * | 1 0  1 0
wx .. xw    ..&#zx |  4  4 |  0  2  4  2  0 |  *  * 24  *  *  * | 0 2  0 0
.. xx ..    ..&#x  |  2  2 |  1  0  2  0  1 |  *  *  * 96  *  * | 0 1  1 0
.x3.x ..    ..     |  0  6 |  0  0  0  3  3 |  *  *  *  * 32  * | 0 1  0 1
.. .x .. *b3.o     |  0  3 |  0  0  0  0  3 |  *  *  *  *  * 32 | 0 0  1 1
-------------------+-------+----------------+-------------------+---------
.. x.3x. *b3o.      12  0 | 12  6  0  0  0 |  4  4  0  0  0  0 | 8 *  * *
wx3xx3xw    ..&#zx  24 24 | 12 12 24 12 12 |  4  0  6 12  4  0 | * 8  * *
.. xx .. *b3oo&#x    3  3 |  3  0  3  0  3 |  0  1  0  3  0  1 | * * 32 *
.x3.x .. *b3.o       0 12 |  0  0  0  6 12 |  0  0  0  0  4  4 | * *  * 8

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