Acronym prit
Name prismatorhombated tesseract,
prismatotruncated hexadecachoron,
runcitruncated hexadecachoron
 
©  
Cross sections
 ©
Circumradius sqrt[(7+3 sqrt(2))/2] = 2.370932
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1x3x3o4x x3x3o .
tut first
x3x . x
hip first
x . o4x
cube first
. x3o4x
sirco first
2 x3x3q . o3u . w u . x4x . u3o4x
3 x3w3o . w3x . x x . u4x . x3x4x
4 u3o3w . o3x . X U . x4x . x3x4x
5 u3q3x . q3u . w o . x4w . u3o4x
6a x3o3W . q3x . X W . o4x . x3o4x
opposite sirco
6b w3u . x w . u4x
7 W3o3x . o3W . w q . x4w  
8a x3q3u . o3w . X W . o4x
8b x3W . x w . u4x
9a w3o3u . w3o . X o . x4w
9b W3x . x
10 o3w3x . W3o . w U . x4x
11a q3x3x . x3q . X x . u4x
11b u3w . x
12 o3x3x .
opposite tut
u3q . w u . x4x
13   x3o . X x . o4x
opposite cube
14 x3w . x  
15 u3o . w
16 x3x . x
opposite hip
(U=qw=u+q=x+w, W=u+w=x+U, X=w+q)
Vertex figure
 ©
Lace city
in approx. ASCII-art
 ©  
    x4o x4x   x4x x4o    
                         
x4o     x4u   x4u     x4o
                         
x4x x4u w4x   w4x x4u x4x
                         
                         
x4x x4u w4x   w4x x4u x4x
                         
x4o     x4u   x4u     x4o
                         
    x4o x4x   x4x x4o    
                  x3x         x3x                  
                                                   
                                                   
         u3o                           u3o         
                  x3w         x3w                  
                                                   
x3o                                             x3o
         u3q                           u3q         
                                                   
                                                   
x3q               u3w         u3w               x3q
         W3o                           W3o         
                                                   
                                                   
w3o               W3x         W3x               w3o
                                                   
o3w               x3W         x3W               o3w
                                                   
                                                   
         o3W                           o3W         
q3x               w3u         w3u               q3x
                                                   
                                                   
         q3u                           q3u         
o3x                                             o3x
                                                   
                  w3x         w3x                  
         o3u                           o3u         
                                                   
                                                   
                  x3x         x3x                  
Coordinates ((1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 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: cube girco hip sirco socco sroh tut
sichado 248008016
prit 2403280016
sirpdo 08320080
)
Dihedral angles
  • at {6} between hip and tut:   150°
  • at {4} between cube and hip:   arccos(-sqrt[2/3]) = 144.735610°
  • at {4} between cube and sirco:   135°
  • at {4} between hip and sirco:   arccos(-1/sqrt(3)) = 125.264390°
  • at {3} between sirco and tut:   120°
Confer
Grünbaumian relatives:
2prit  
uniform relative:
gircope  
related CRFs:
sircoa gircotum   owau prit   pex thex   pabex thex   pacprit  
decompositions:
thex || prit   sidpith || prit  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope prit is isomorphic to paqrit, thereby replacing sirco by querco.

Note that prit can be thought of as the external blend of 1 thex + 16 tuttips + 32 thiddips + 24 squippyps + 8 octasircos. This decomposition is described as the degenerate segmentoteron xx3xx3oo4ox&#x. – Alternatively it could also be decomposed into 1 sidpith + 16 tetatuts + 32 tricupes + 24 teses + 8 cubasircoes, as described by xx3ox3oo4xx&#x. – Further, even so subdimensioanlly degenerate, prit could also be decomposed into 1 tat + 16 tetaltuts + 32 hippyps + 24 squicufs + 8 sircoatics, as described by ox3ox3xo4xx&#x.


Incidence matrix according to Dynkin symbol

x3x3o4x

. . . . | 192 |  1   2   2 |  2  2  1  2  1 |  1  2  1 1
--------+-----+------------+----------------+-----------
x . . . |   2 | 96   *   * |  2  2  0  0  0 |  1  2  1 0
. x . . |   2 |  * 192   * |  1  0  1  1  0 |  1  1  0 1
. . . x |   2 |  *   * 192 |  0  1  0  1  1 |  0  1  1 1
--------+-----+------------+----------------+-----------
x3x . . |   6 |  3   3   0 | 64  *  *  *  * |  1  1  0 0
x . . x |   4 |  2   0   2 |  * 96  *  *  * |  0  1  1 0
. x3o . |   3 |  0   3   0 |  *  * 64  *  * |  1  0  0 1
. x . x |   4 |  0   2   2 |  *  *  * 96  * |  0  1  0 1
. . o4x |   4 |  0   0   4 |  *  *  *  * 48 |  0  0  1 1
--------+-----+------------+----------------+-----------
x3x3o .   12 |  6  12   0 |  4  0  4  0  0 | 16  *  * *
x3x . x   12 |  6   6   6 |  2  3  0  3  0 |  * 32  * *
x . o4x    8 |  4   0   8 |  0  4  0  0  2 |  *  * 24 *
. x3o4x   24 |  0  24  24 |  0  0  8 12  6 |  *  *  * 8

snubbed forms: β3x3o4x, x3β3o4x, x3x3o4s, β3β3o4x, β3x3o4β, x3β3o4β, β3β3o4β

x3x3/2o4/3x

. .   .   . | 192 |  1   2   2 |  2  2  1  2  1 |  1  2  1 1
------------+-----+------------+----------------+-----------
x .   .   . |   2 | 96   *   * |  2  2  0  0  0 |  1  2  1 0
. x   .   . |   2 |  * 192   * |  1  0  1  1  0 |  1  1  0 1
. .   .   x |   2 |  *   * 192 |  0  1  0  1  1 |  0  1  1 1
------------+-----+------------+----------------+-----------
x3x   .   . |   6 |  3   3   0 | 64  *  *  *  * |  1  1  0 0
x .   .   x |   4 |  2   0   2 |  * 96  *  *  * |  0  1  1 0
. x3/2o   . |   3 |  0   3   0 |  *  * 64  *  * |  1  0  0 1
. x   .   x |   4 |  0   2   2 |  *  *  * 96  * |  0  1  0 1
. .   o4/3x |   4 |  0   0   4 |  *  *  *  * 48 |  0  0  1 1
------------+-----+------------+----------------+-----------
x3x3/2o   .   12 |  6  12   0 |  4  0  4  0  0 | 16  *  * *
x3x   .   x   12 |  6   6   6 |  2  3  0  3  0 |  * 32  * *
x .   o4/3x    8 |  4   0   8 |  0  4  0  0  2 |  *  * 24 *
. x3/2o4/3x   24 |  0  24  24 |  0  0  8 12  6 |  *  *  * 8

xuxxux3ooxxoo4xxxxxx&#xt   → all non-central heights = 1/sqrt(2) = 0.707107
                             central height = 1
(sirco || pseudo (u,x)-sirco || pseudo girco || pseudo girco || pseudo (u,x)-sirco || sirco)

o.....3o.....4o.....      & | 48  *  * |  2  2  1  0  0  0  0  0  0 |  1  2  1  2  2  0  0  0  0  0  0  0  0 | 1  1  1  2 0 0  0
.o....3.o....4.o....      & |  * 48  * |  0  0  1  2  2  0  0  0  0 |  0  0  0  2  2  1  1  2  0  0  0  0  0 | 0  1  1  2 1 0  0
..o...3..o...4..o...      & |  *  * 96 |  0  0  0  0  1  1  1  1  1 |  0  0  0  0  1  0  1  1  1  1  1  1  1 | 0  0  1  1 1 1  1
----------------------------+----------+----------------------------+----------------------------------------+------------------
x..... ...... ......      & |  2  0  0 | 48  *  *  *  *  *  *  *  * |  1  1  0  0  1  0  0  0  0  0  0  0  0 | 1  0  1  1 0 0  0
...... ...... x.....      & |  2  0  0 |  * 48  *  *  *  *  *  *  * |  0  1  1  1  0  0  0  0  0  0  0  0  0 | 1  1  0  1 0 0  0
oo....3oo....4oo....&#x   & |  1  1  0 |  *  * 48  *  *  *  *  *  * |  0  0  0  2  2  0  0  0  0  0  0  0  0 | 0  1  1  2 0 0  0
...... ...... .x....      & |  0  2  0 |  *  *  * 48  *  *  *  *  * |  0  0  0  1  0  1  0  1  0  0  0  0  0 | 0  1  0  1 1 0  0
.oo...3.oo...4.oo...&#x   & |  0  1  1 |  *  *  *  * 96  *  *  *  * |  0  0  0  0  1  0  1  1  0  0  0  0  0 | 0  0  1  1 1 0  0
..x... ...... ......      & |  0  0  2 |  *  *  *  *  * 48  *  *  * |  0  0  0  0  1  0  0  0  1  1  1  0  0 | 0  0  1  1 0 1  1
...... ..x... ......      & |  0  0  2 |  *  *  *  *  *  * 48  *  * |  0  0  0  0  0  0  1  0  1  0  0  1  0 | 0  0  1  0 1 1  0
...... ...... ..x...      & |  0  0  2 |  *  *  *  *  *  *  * 48  * |  0  0  0  0  0  0  0  1  0  1  0  0  1 | 0  0  0  1 1 0  1
..oo..3..oo..4..oo..&#x     |  0  0  2 |  *  *  *  *  *  *  *  * 48 |  0  0  0  0  0  0  0  0  0  0  1  1  1 | 0  0  0  0 1 1  1
----------------------------+----------+----------------------------+----------------------------------------+------------------
x.....3o..... ......      & |  3  0  0 |  3  0  0  0  0  0  0  0  0 | 16  *  *  *  *  *  *  *  *  *  *  *  * | 1  0  1  0 0 0  0
x..... ...... x.....      & |  4  0  0 |  2  2  0  0  0  0  0  0  0 |  * 24  *  *  *  *  *  *  *  *  *  *  * | 1  0  0  1 0 0  0
...... o.....4x.....      & |  4  0  0 |  0  4  0  0  0  0  0  0  0 |  *  * 12  *  *  *  *  *  *  *  *  *  * | 1  1  0  0 0 0  0
...... ...... xx....&#x   & |  2  2  0 |  0  1  2  1  0  0  0  0  0 |  *  *  * 48  *  *  *  *  *  *  *  *  * | 0  1  0  1 0 0  0
xux... ...... ......&#xt  & |  2  2  2 |  1  0  2  0  2  1  0  0  0 |  *  *  *  * 48  *  *  *  *  *  *  *  * | 0  0  1  1 0 0  0
...... .o....4.x....      & |  0  4  0 |  0  0  0  4  0  0  0  0  0 |  *  *  *  *  * 12  *  *  *  *  *  *  * | 0  1  0  0 1 0  0
...... .ox... ......&#x   & |  0  1  2 |  0  0  0  0  2  0  1  0  0 |  *  *  *  *  *  * 48  *  *  *  *  *  * | 0  0  1  0 1 0  0
...... ...... .xx...&#x   & |  0  2  2 |  0  0  0  1  2  0  0  1  0 |  *  *  *  *  *  *  * 48  *  *  *  *  * | 0  0  0  1 1 0  0
..x...3..x... ......      & |  0  0  6 |  0  0  0  0  0  3  3  0  0 |  *  *  *  *  *  *  *  * 16  *  *  *  * | 0  0  1  0 0 1  0
..x... ...... ..x...      & |  0  0  4 |  0  0  0  0  0  2  0  2  0 |  *  *  *  *  *  *  *  *  * 24  *  *  * | 0  0  0  1 0 0  1
..xx.. ...... ......&#x     |  0  0  4 |  0  0  0  0  0  2  0  0  2 |  *  *  *  *  *  *  *  *  *  * 24  *  * | 0  0  0  0 0 1  1
...... ..xx.. ......&#x     |  0  0  4 |  0  0  0  0  0  0  2  0  2 |  *  *  *  *  *  *  *  *  *  *  * 24  * | 0  0  0  0 1 1  0
...... ...... ..xx..&#x     |  0  0  4 |  0  0  0  0  0  0  0  2  2 |  *  *  *  *  *  *  *  *  *  *  *  * 24 | 0  0  0  0 1 0  1
----------------------------+----------+----------------------------+----------------------------------------+------------------
x.....3o.....4x.....      &  24  0  0 | 24 24  0  0  0  0  0  0  0 |  8 12  6  0  0  0  0  0  0  0  0  0  0 | 2  *  *  * * *  *
...... oo....4xx....&#x   &   4  4  0 |  0  4  4  4  0  0  0  0  0 |  0  0  1  4  0  1  0  0  0  0  0  0  0 | * 12  *  * * *  *
xux...3oox... ......&#xt  &   3  3  6 |  3  0  3  0  6  3  3  0  0 |  1  0  0  0  3  0  3  0  1  0  0  0  0 | *  * 16  * * *  *
xux... ...... xxx...&#xt  &   4  4  4 |  2  2  4  2  4  2  0  2  0 |  0  1  0  2  2  0  0  2  0  1  0  0  0 | *  *  * 24 * *  *
...... .oxxo.4.xxxx.&#xt      0  8 16 |  0  0  0  8 16  0  8  8  8 |  0  0  0  0  0  2  8  8  0  0  0  4  4 | *  *  *  * 6 *  *
..xx..3..xx.. ......&#x       0  0 12 |  0  0  0  0  0  6  6  0  6 |  0  0  0  0  0  0  0  0  2  0  3  3  0 | *  *  *  * * 8  *
..xx.. ...... ..xx..&#x       0  0  8 |  0  0  0  0  0  4  0  4  4 |  0  0  0  0  0  0  0  0  0  2  2  0  2 | *  *  *  * * * 12

qo3xx3oq *b3xx&#zx   → height = 0
(tegum sum of 2 mutually gyrated (x,x,q)-tahs)

o.3o.3o. *b3o.     | 96  * |  2  1   2  0  0 |  1  2  1  2  2  0  0 | 1 1  1  2 0
.o3.o3.o *b3.o     |  * 96 |  0  0   2  2  1 |  0  0  1  2  2  1  2 | 0 1  1  2 1
-------------------+-------+-----------------+----------------------+------------
.. x. ..    ..     |  2  0 | 96  *   *  *  * |  1  1  0  1  0  0  0 | 1 1  0  1 0
.. .. ..    x.     |  2  0 |  * 48   *  *  * |  0  2  0  0  2  0  0 | 1 0  1  2 0
oo3oo3oo *b3oo&#x  |  1  1 |  *  * 192  *  * |  0  0  1  1  1  0  0 | 0 1  1  1 0
.. .x ..    ..     |  0  2 |  *  *   * 96  * |  0  0  0  1  0  1  1 | 0 1  0  1 1
.. .. ..    .x     |  0  2 |  *  *   *  * 48 |  0  0  0  0  2  0  2 | 0 0  1  2 1
-------------------+-------+-----------------+----------------------+------------
.. x.3o.    ..     |  3  0 |  3  0   0  0  0 | 32  *  *  *  *  *  * | 1 1  0  0 0
.. x. .. *b3x.     |  6  0 |  3  3   0  0  0 |  * 32  *  *  *  *  * | 1 0  0  1 0
qo .. oq    ..&#zx |  2  2 |  0  0   4  0  0 |  *  * 48  *  *  *  * | 0 1  1  0 0
.. xx ..    ..&#x  |  2  2 |  1  0   2  1  0 |  *  *  * 96  *  *  * | 0 1  0  1 0
.. .. ..    xx&#x  |  2  2 |  0  1   2  0  1 |  *  *  *  * 96  *  * | 0 0  1  1 0
.o3.x ..    ..     |  0  3 |  0  0   0  3  0 |  *  *  *  *  * 32  * | 0 1  0  0 1
.. .x .. *b3.x     |  0  6 |  0  0   0  3  3 |  *  *  *  *  *  * 32 | 0 0  0  1 1
-------------------+-------+-----------------+----------------------+------------
.. x.3o. *b3x.      12  0 | 12  6   0  0  0 |  4  4  0  0  0  0  0 | 8 *  *  * *
qo3xx3oq    ..&#zx  12 12 | 12  0  24 12  0 |  4  0  6 12  0  4  0 | * 8  *  * *
qo .. oq    xx&#zx   4  4 |  0  2   8  0  2 |  0  0  2  0  4  0  0 | * * 24  * *
.. xx .. *b3xx&#x    6  6 |  3  3   6  3  3 |  0  1  0  3  3  0  1 | * *  * 32 *
.o3.x .. *b3.x       0 12 |  0  0   0 12  6 |  0  0  0  0  0  4  4 | * *  *  * 8

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