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 . xtrip first o . x4x{8} first . x3x4xgirco 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 . x3x4xopposite 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 . x4xopposite {8} 14 x3x . X 15 u3o . w 16 x3o . xopposite 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°
Confer
Grünbaumian relatives:
2grit
decompositions:
tah || grit   tat || grit
general polytopal classes:
partial Stott expansions
External

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
```

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