Acronym prissi
Name prismatorhombisnub icositetrachoron,
prismato-semistruncated icositetrachoron,
runcic snub icositetrachoron
 
 ©
Circumradius sqrt[4+sqrt(5)] = 2.497212
Vertex figure
 ©
Coordinates
  • (0, 1/2, (1+sqrt(5))/4, (7+sqrt(5))/4)           & all even permutations, all changes of sign
  • (1/2, 1, (3+sqrt(5))/4, (5+sqrt(5))/4)           & all even permutations, all changes of sign
Confer
uniform relatives:
sadi   ico  
related CRFs:
icau prissi  
general polytopal classes:
scaliform  
External
links
hedrondude   wikipedia   quickfur  

As abstract polytope prissi is isomorphic to prarsi, thereby replacing prograde squares by retrogrades, respectively ike by gike.

This is a scaliform polychoron, obtained as a variation of a faceting of the prismatorhombated icositetrachoron (prico). Or as a Stott addition of the snub icositetrachoron (sadi) with the icositetrachoron (ico) resulting in shifting formerly face-connected icosahedra (ike) one edge length appart.

Moreover it can be obtained by chopping off all but 288 vertices of padohi. This could be seen best from the vertex figure of padohi: vo5ox&#q, of which the vertex figure of prissi is a faceting.

Prissi can also be considered as the double application of an alternated faceting according to x3x4x3x (gippic) → x3x4s3s (prico) = x3x4o3x → s'3s'4s3s = s3s4o3x. (Because of the intrinsic symmetry of the symbol x3x4x3x, the application order (s first or s' first) obviously is irrelevant.)


Incidence matrix according to Dynkin symbol

s3s4o3x

demi( . . . . ) | 288 |   2   1   4 |  1   2   3   4  2 |  1  2  1  3
----------------+-----+-------------+-------------------+------------
demi( . . . x ) |   2 | 288   *   * |  1   0   0   2  1 |  0  1  1  2
      . s4o .   |   2 |   * 144   * |  0   0   2   0  2 |  1  0  1  2
sefa( s3s . . ) |   2 |   *   * 576 |  0   1   1   1  0 |  1  1  0  1
----------------+-----+-------------+-------------------+------------
demi( . . o3x ) |   3 |   3   0   0 | 96   *   *   *  * |  0  0  1  1
      s3s . .      3 |   0   0   3 |  * 192   *   *  * |  1  1  0  0
sefa( s3s4o . ) |   3 |   0   1   2 |  *   * 288   *  * |  1  0  0  1
sefa( s3s 2 x ) |   4 |   2   0   2 |  *   *   * 288  * |  0  1  0  1
sefa( . s4o3x ) |   6 |   3   3   0 |  *   *   *   * 96 |  0  0  1  1
----------------+-----+-------------+-------------------+------------
      s3s4o .     12 |   0   6  24 |  0   8  12   0  0 | 24  *  *  *
      s3s 2 x      6 |   3   0   6 |  0   2   0   3  0 |  * 96  *  *
      . s4o3x     12 |  12   6   0 |  4   0   0   0  4 |  *  * 24  *
sefa( s3s4o3x )    9 |   6   3   6 |  1   0   3   3  1 |  *  *  * 96

starting figure: x3x4o3x

fox3xxx3xfo *b3oxf&#zx   → height = 0

o..3o..3o.. *b3o..     | 96  *  * |  2  1   2   2  0  0   0  0  0 |  2  1  2  1  2  2   2  0  0  0  0  0  0 | 1  1  2  1  2 0  0 0
.o.3.o.3.o. *b3.o.     |  * 96  * |  0  0   2   0  2  1   2  0  0 |  0  0  2  2  0  0   2  1  2  1  2  0  0 | 0  2  0  1  2 1  1 0
..o3..o3..o *b3..o     |  *  * 96 |  0  0   0   2  0  0   2  1  2 |  0  0  0  0  2  1   2  0  0  2  2  2  1 | 0  0  1  1  2 0  2 1
-----------------------+----------+-------------------------------+-----------------------------------------+---------------------
... x.. ...    ...     |  2  0  0 | 96  *   *   *  *  *   *  *  * |  1  1  1  0  1  0   0  0  0  0  0  0  0 | 1  1  1  0  1 0  0 0
... ... x..    ...     |  2  0  0 |  * 48   *   *  *  *   *  *  * |  2  0  0  0  0  2   0  0  0  0  0  0  0 | 1  0  2  1  0 0  0 0
oo.3oo.3oo. *b3oo.&#x  |  1  1  0 |  *  * 192   *  *  *   *  *  * |  0  0  1  1  0  0   1  0  0  0  0  0  0 | 0  1  0  1  1 0  0 0
o.o3o.o3o.o *b3o.o&#x  |  1  0  1 |  *  *   * 192  *  *   *  *  * |  0  0  0  0  1  1   1  0  0  0  0  0  0 | 0  0  1  1  1 0  0 0
... .x. ...    ...     |  0  2  0 |  *  *   *   * 96  *   *  *  * |  0  0  1  0  0  0   0  1  1  0  1  0  0 | 0  1  0  0  1 1  1 0
... ... ...    .x.     |  0  2  0 |  *  *   *   *  * 48   *  *  * |  0  0  0  2  0  0   0  0  2  0  0  0  0 | 0  2  0  1  0 1  0 0
.oo3.oo3.oo *b3.oo&#x  |  0  1  1 |  *  *   *   *  *  * 192  *  * |  0  0  0  0  0  0   1  0  0  1  1  0  0 | 0  0  0  1  1 0  1 0
..x ... ...    ...     |  0  0  2 |  *  *   *   *  *  *   * 48  * |  0  0  0  0  0  0   0  0  0  2  0  2  0 | 0  0  0  1  0 0  2 1
... ..x ...    ...     |  0  0  2 |  *  *   *   *  *  *   *  * 96 |  0  0  0  0  1  0   0  0  0  0  1  1  1 | 0  0  1  0  1 0  1 1
-----------------------+----------+-------------------------------+-----------------------------------------+---------------------
... x..3x..    ...     |  6  0  0 |  3  3   0   0  0  0   0  0  0 | 32  *  *  *  *  *   *  *  *  *  *  *  * | 1  0  1  0  0 0  0 0
... x.. ... *b3o..     |  3  0  0 |  3  0   0   0  0  0   0  0  0 |  * 32  *  *  *  *   *  *  *  *  *  *  * | 1  1  0  0  0 0  0 0
... xx. ...    ...&#x  |  2  2  0 |  1  0   2   0  1  0   0  0  0 |  *  * 96  *  *  *   *  *  *  *  *  *  * | 0  1  0  0  1 0  0 0
... ... ...    ox.&#x  |  1  2  0 |  0  0   2   0  0  1   0  0  0 |  *  *  * 96  *  *   *  *  *  *  *  *  * | 0  1  0  1  0 0  0 0
... x.x ...    ...&#x  |  2  0  2 |  1  0   0   2  0  0   0  0  1 |  *  *  *  * 96  *   *  *  *  *  *  *  * | 0  0  1  0  1 0  0 0
... ... x.o    ...&#x  |  2  0  1 |  0  1   0   2  0  0   0  0  0 |  *  *  *  *  * 96   *  *  *  *  *  *  * | 0  0  1  1  0 0  0 0
ooo3ooo3ooo *b3ooo&#x  |  1  1  1 |  0  0   1   1  0  0   1  0  0 |  *  *  *  *  *  * 192  *  *  *  *  *  * | 0  0  0  1  1 0  0 0
.o.3.x. ...    ...     |  0  3  0 |  0  0   0   0  3  0   0  0  0 |  *  *  *  *  *  *   * 32  *  *  *  *  * | 0  0  0  0  0 1  1 0
... .x. ... *b3.x.     |  0  6  0 |  0  0   0   0  3  3   0  0  0 |  *  *  *  *  *  *   *  * 32  *  *  *  * | 0  1  0  0  0 1  0 0
.ox ... ...    ...&#x  |  0  1  2 |  0  0   0   0  0  0   2  1  0 |  *  *  *  *  *  *   *  *  * 96  *  *  * | 0  0  0  1  0 0  1 0
... .xx ...    ...&#x  |  0  2  2 |  0  0   0   0  1  0   2  0  1 |  *  *  *  *  *  *   *  *  *  * 96  *  * | 0  0  0  0  1 0  1 0
..x3..x ...    ...     |  0  0  6 |  0  0   0   0  0  0   0  3  3 |  *  *  *  *  *  *   *  *  *  *  * 32  * | 0  0  0  0  0 0  1 1
... ..x3..o    ...     |  0  0  3 |  0  0   0   0  0  0   0  0  3 |  *  *  *  *  *  *   *  *  *  *  *  * 32 | 0  0  1  0  0 0  0 1
-----------------------+----------+-------------------------------+-----------------------------------------+---------------------
... x..3x.. *b3o..      12  0  0 | 12  6   0   0  0  0   0  0  0 |  4  4  0  0  0  0   0  0  0  0  0  0  0 | 8  *  *  *  * *  * *
... xx. ... *b3ox.&#x    3  6  0 |  3  0   6   0  3  3   0  0  0 |  0  1  3  3  0  0   0  0  1  0  0  0  0 | * 32  *  *  * *  * *
... x.x3x.o    ...&#x    6  0  3 |  3  3   0   6  0  0   0  0  3 |  1  0  0  0  3  3   0  0  0  0  0  0  1 | *  * 32  *  * *  * *
fox ... xfo    oxf&#zx   4  4  4 |  0  2   8   8  0  2   8  2  0 |  0  0  0  4  0  4   8  0  0  4  0  0  0 | *  *  * 24  * *  * *
... xxx ...    ...&#x    2  2  2 |  1  0   2   2  1  0   2  0  1 |  0  0  1  0  1  0   2  0  0  0  1  0  0 | *  *  *  * 96 *  * *
.o.3.x. ... *b3.x.       0 12  0 |  0  0   0   0 12  6   0  0  0 |  0  0  0  0  0  0   0  4  4  0  0  0  0 | *  *  *  *  * 8  * *
.ox3.xx ...    ...&#x    0  3  6 |  0  0   0   0  3  0   6  3  3 |  0  0  0  0  0  0   0  1  0  3  3  1  0 | *  *  *  *  * * 32 *
..x3..x3..o    ...       0  0 12 |  0  0   0   0  0  0   0  6 12 |  0  0  0  0  0  0   0  0  0  0  0  4  4 | *  *  *  *  * *  * 8

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