Acronym	prit
Name	prismatorhombated tesseract, prismatotruncated hexadecachoron, runcitruncated hexadecachoron
	©   ©
Net	©
Cross sections	©
Circumradius	sqrt[(7+3 sqrt(2))/2] = 2.370932
Vertex layers	Layer Symmetry Subsymmetries   o3o3o4o o3o3o . o3o . o o . o4o . o3o4o 1 x3x3o4x 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 24 8 0 0 8 0 16 prit 24 0 32 8 0 0 16 sirpdo 0 8 32 0 0 8 0 )
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°
Face vector	192, 480, 368, 80
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: Wythoffian polychora   partial Stott expansions
External links

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, although 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