Acronym tat
Name truncated tesseract
 
Cross sections 
 ©
Circumradius sqrt[(5+3 sqrt(2))/2] = 2.149726
Vertex figure 
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Vertex layers
LayerSymmetrySubsymmetries
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1o3o3x4x o3o3x .
tet first		 o3o . x
edge first		 o . x4x
{8} first		 . o3x4x
tic first
2 o3o3w . o3x . w x . o4w . o3o4w
3 o3x3w . o3w . w w . o4w . o3o4w
4 o3w3x . o3W . x W . x4x . o3x4x
opposite tic
5 x3w3o . x3w . w w . o4w  
6 w3x3o . w3x . w x . o4w
7 w3o3o . W3o . x o . x4x
opposite {8}
8 x3o3o .
opposite tet		 w3o . w  
9   x3o . w
10 o3o . x
opposite edge
(W=qw=u+q=x+w)
Lace city
in approx. ASCII-art 
 ©  

x4x w4o   w4o x4x
                 
w4o           w4o
                 
                 
w4o           w4o
                 
x4x w4o   w4o x4x

   x3o w3o   w3x x3w   o3w o3x   
                                 
                                 
o3o       W3o       o3W       o3o
                                 
                                 
                                 
o3o       W3o       o3W       o3o
                                 
                                 
   x3o w3o   w3x x3w   o3w o3x
Coordinates ((1+sqrt(2))/2, (1+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: tet tic
tat 168
)
Confer
blends:
otbott  
External
links 		hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope tat is isomorphic to quitit, thereby replacing the octagons by octagrams, resp. replacing tic by quith.


Incidence matrix according to Dynkin symbol

o3o3x4x

. . . . | 64 |  3  1 |  3  3 |  1 3
--------+----+-------+-------+-----
. . x . |  2 | 96  * |  2  1 |  1 2
. . . x |  2 |  * 32 |  0  3 |  0 3
--------+----+-------+-------+-----
. o3x . |  3 |  3  0 | 64  * |  1 1
. . x4x |  8 |  4  4 |  * 24 |  0 2
--------+----+-------+-------+-----
o3o3x . ♦  4 |  6  0 |  4  0 | 16 *
. o3x4x ♦ 24 | 24 12 |  8  6 |  * 8


o3o3/2x4x

. .   . . | 64 |  3  1 |  3  3 |  1 3
----------+----+-------+-------+-----
. .   x . |  2 | 96  * |  2  1 |  1 2
. .   . x |  2 |  * 32 |  0  3 |  0 3
----------+----+-------+-------+-----
. o3/2x . |  3 |  3  0 | 64  * |  1 1
. .   x4x |  8 |  4  4 |  * 24 |  0 2
----------+----+-------+-------+-----
o3o3/2x . ♦  4 |  6  0 |  4  0 | 16 *
. o3/2x4x ♦ 24 | 24 12 |  8  6 |  * 8


o3/2o3x4x

.   . . . | 64 |  3  1 |  3  3 |  1 3
----------+----+-------+-------+-----
.   . x . |  2 | 96  * |  2  1 |  1 2
.   . . x |  2 |  * 32 |  0  3 |  0 3
----------+----+-------+-------+-----
.   o3x . |  3 |  3  0 | 64  * |  1 1
.   . x4x |  8 |  4  4 |  * 24 |  0 2
----------+----+-------+-------+-----
o3/2o3x . ♦  4 |  6  0 |  4  0 | 16 *
.   o3x4x ♦ 24 | 24 12 |  8  6 |  * 8


o3/2o3/2x4x

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


oooo3xoox4xwwx&#xt   → outer heights = 1/sqrt(2) = 0.707107
                       inner height = 1

o...3o...4o...     | 24 * *  * |  2  1  1 0  0  0  0 | 1 2  2  1  0 0 0 | 1 1 2 0 0
.o..3.o..4.o..     |  * 8 *  * |  0  0  3 1  0  0  0 | 0 0  3  3  0 0 0 | 0 1 3 0 0
..o.3..o.4..o.     |  * * 8  * |  0  0  0 1  3  0  0 | 0 0  0  3  3 0 0 | 0 0 3 1 0
...o3...o4...o     |  * * * 24 |  0  0  0 0  1  2  1 | 0 0  0  1  2 1 2 | 0 0 2 1 1
-------------------+-----------+---------------------+------------------+----------
.... x... ....     |  2 0 0  0 | 24  *  * *  *  *  * | 1 1  1  0  0 0 0 | 1 1 1 0 0
.... .... x...     |  2 0 0  0 |  * 12  * *  *  *  * | 0 2  0  1  0 0 0 | 1 0 2 0 0
oo..3oo..4oo..&#x  |  1 1 0  0 |  *  * 24 *  *  *  * | 0 0  2  1  0 0 0 | 0 1 2 0 0
.oo.3.oo.4.oo.&#x  |  0 1 1  0 |  *  *  * 8  *  *  * | 0 0  0  3  0 0 0 | 0 0 3 0 0
..oo3..oo4..oo&#x  |  0 0 1  1 |  *  *  * * 24  *  * | 0 0  0  1  2 0 0 | 0 0 2 1 0
.... ...x ....     |  0 0 0  2 |  *  *  * *  * 24  * | 0 0  0  0  1 1 1 | 0 0 1 1 1
.... .... ...x     |  0 0 0  2 |  *  *  * *  *  * 12 | 0 0  0  1  0 0 2 | 0 0 2 0 1
-------------------+-----------+---------------------+------------------+----------
o...3x... ....     |  3 0 0  0 |  3  0  0 0  0  0  0 | 8 *  *  *  * * * | 1 1 0 0 0
.... x...4x...     |  8 0 0  0 |  4  4  0 0  0  0  0 | * 6  *  *  * * * | 1 0 1 0 0
.... xo.. ....&#x  |  2 1 0  0 |  1  0  2 0  0  0  0 | * * 24  *  * * * | 0 1 1 0 0
.... .... xwwx&#xt |  2 2 2  2 |  0  1  2 2  2  0  1 | * *  * 12  * * * | 0 0 2 0 0
.... ..ox ....&#x  |  0 0 1  2 |  0  0  0 0  2  1  0 | * *  *  * 24 * * | 0 0 1 1 0
...o3...x ....     |  0 0 0  3 |  0  0  0 0  0  3  0 | * *  *  *  * 8 * | 0 0 0 1 1
.... ...x4...x     |  0 0 0  8 |  0  0  0 0  0  4  4 | * *  *  *  * * 6 | 0 0 1 0 1
-------------------+-----------+---------------------+------------------+----------
o...3x...4x...     ♦ 24 0 0  0 | 24 12  0 0  0  0  0 | 8 6  0  0  0 0 0 | 1 * * * *
oo..3xo.. ....&#x  ♦  3 1 0  0 |  3  0  3 0  0  0  0 | 1 0  3  0  0 0 0 | * 8 * * *
.... xoox4xwwx&#xt ♦  8 4 4  8 |  4  4  8 4  8  4  4 | 0 1  4  4  4 0 1 | * * 6 * *
..oo3..ox ....&#x  ♦  0 0 1  3 |  0  0  0 0  3  3  0 | 0 0  0  0  3 1 0 | * * * 8 *
...o3...x4...x     ♦  0 0 0 24 |  0  0  0 0  0 24 12 | 0 0  0  0  0 8 6 | * * * * 1

or
o...3o...4o...     & | 48  * |  2  1  1 0 |  1  2  2  1 | 1  1 2
.o..3.o..4.o..     & |  * 16 |  0  0  3 1 |  0  0  3  3 | 0  1 3
---------------------+-------+------------+-------------+-------
.... x... ....     & |  2  0 | 48  *  * * |  1  1  1  0 | 1  1 1
.... .... x...     & |  2  0 |  * 24  * * |  0  2  0  1 | 1  0 2
oo..3oo..4oo..&#x  & |  1  1 |  *  * 48 * |  0  0  2  1 | 0  1 2
.oo.3.oo.4.oo.&#x    |  0  2 |  *  *  * 8 |  0  0  0  3 | 0  0 3
---------------------+-------+------------+-------------+-------
o...3x... ....     & |  3  0 |  3  0  0 0 | 16  *  *  * | 1  1 0
.... x...4x...     & |  8  0 |  4  4  0 0 |  * 12  *  * | 1  0 1
.... xo.. ....&#x  & |  2  1 |  1  0  2 0 |  *  * 48  * | 0  1 1
.... .... xwwx&#xt   |  4  4 |  0  2  4 2 |  *  *  * 12 | 0  0 2
---------------------+-------+------------+-------------+-------
o...3x...4x...     & ♦ 24  0 | 24 12  0 0 |  8  6  0  0 | 2  * *
oo..3xo.. ....&#x  & ♦  3  1 |  3  0  3 0 |  1  0  3  0 | * 16 *
.... xoox4xwwx&#xt   ♦ 16  8 |  8  8 16 4 |  0  2  8  4 | *  * 6


xwwxoooo3ooxwwxoo3ooooxwwx&#xt   → height(1,2) = height(3,4) = height(5,6) = height(7,8) = 1/2
                       height(2,3) = height(4,5) = height(6,7) = 1/sqrt(2) = 0.707107
(tet || pseudo w-tet || pseudo (w,x)-tut || pseudo (x,w)-tut || pseudo inv (x,w)-tut || pseudo inv (w,x)-tut || pseudo dual w-tet || dual tet)

o.......3o.......3o.......      & | 8 *  *  * |  3 1  0  0  0  0  0 | 3  3  0 0  0  0 | 1 3 0 0
.o......3.o......3.o......      & | * 8  *  * |  0 1  3  0  0  0  0 | 0  3  3 0  0  0 | 0 3 1 0
..o.....3..o.....3..o.....      & | * * 24  * |  0 0  1  2  1  0  0 | 0  1  2 1  2  0 | 0 3 1 0
...o....3...o....3...o....      & | * *  * 24 |  0 0  0  0  1  1  2 | 0  1  0 0  2  3 | 0 3 0 1
----------------------------------+-----------+---------------------+-----------------+--------
x....... ........ ........      & | 2 0  0  0 | 12 *  *  *  *  *  * | 2  1  0 0  0  0 | 1 2 0 0
oo......3oo......3oo......&#x   & | 1 1  0  0 |  * 8  *  *  *  *  * | 0  3  0 0  0  0 | 0 3 0 0
.oo.....3.oo.....3.oo.....&#x   & | 0 1  1  0 |  * * 24  *  *  *  * | 0  1  2 0  0  0 | 0 2 1 0
........ ..x..... ........      & | 0 0  2  0 |  * *  * 24  *  *  * | 0  0  1 1  1  0 | 0 2 1 0
..oo....3..oo....3..oo....&#x   & | 0 0  1  1 |  * *  *  * 24  *  * | 0  1  0 0  2  0 | 0 3 0 0
...x.... ........ ........      & | 0 0  0  2 |  * *  *  *  * 12  * | 0  1  0 0  0  2 | 0 2 0 1
...oo...3...oo...3...oo...&#x     | 0 0  0  2 |  * *  *  *  *  * 24 | 0  0  0 0  1  2 | 0 2 0 1
----------------------------------+-----------+---------------------+-----------------+--------
x.......3o....... ........      & | 3 0  0  0 |  3 0  0  0  0  0  0 | 8  *  * *  *  * | 1 1 0 0
xwwx.... ........ ........&#xt  & | 2 2  2  2 |  1 2  2  0  2  1  0 | * 12  * *  *  * | 0 2 0 0
........ .ox..... ........&#x   & | 0 1  2  0 |  0 0  2  1  0  0  0 | *  * 24 *  *  * | 0 1 1 0
........ ..x.....3..o.....      & | 0 0  3  0 |  0 0  0  3  0  0  0 | *  *  * 8  *  * | 0 1 1 0
........ ..xwwx.. ........&#xt    | 0 0  4  4 |  0 0  0  2  4  0  2 | *  *  * * 12  * | 0 2 0 0
...xo... ........ ........&#x   & | 0 0  0  3 |  0 0  0  0  0  1  2 | *  *  * *  * 24 | 0 1 0 1
----------------------------------+-----------+---------------------+-----------------+--------
x.......3o.......3o.......      & ♦ 4 0  0  0 |  6 0  0  0  0  0  0 | 4  0  0 0  0  0 | 2 * * *
xwwxoo..3ooxwwx.. ........&#xt  & ♦ 3 3  9  9 |  3 3  6  6  9  3  6 | 1  3  3 1  3  3 | * 8 * *
........ .ox.....3.oo.....&#x   & ♦ 0 1  3  0 |  0 0  3  3  0  0  0 | 0  0  3 1  0  0 | * * 8 *
...xo... ........ ...ox...&#x     ♦ 0 0  0  4 |  0 0  0  0  0  2  4 | 0  0  0 0  0  4 | * * * 6

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