Acronym	grit
Name	great rhombated tesseract, cantitruncated tesseract
	©
Cross sections	©
Circumradius	sqrt[(11+5 sqrt(2))/2] = 3.005916
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o4o o3o3o . o3o . o o . o4o . o3o4o 1 o3x3x4x 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 8 32 16 )
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°
Face vector	192, 384, 248, 56
Confer	Grünbaumian relatives: 2grit   decompositions: tah || grit   tat || grit   general polytopal classes: Wythoffian polychora   partial Stott expansions
External links

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, although subdimensioanlly degenerate, grit can be decomposed into 1 prit + 16 tutas + 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