Acronym quappin
Name quasiprismated penteract
Circumradius sqrt(2)-1/2 = 0.914214
Coordinates (sqrt(2)-1, sqrt(2)-1, 1, 1, 1)/2   & all permutations, all changes of sign
Colonel of regiment fawdint
Face vector 320, 1440, 2160, 1240, 202
Confer
general polytopal classes:
Wythoffian polytera  
External
links 		polytopewiki  

As abstract polytope quappin is isomorphic to span, thereby replacing quidpith by sidpith.


Incidence matrix according to Dynkin symbol

o3x3o3o4/3x

. . . .   . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
------------+-----+---------+-----------------+------------------------+------------
. x . .   . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
. . . .   x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
------------+-----+---------+-----------------+------------------------+------------
o3x . .   . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
. x3o .   . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
. x . .   x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
. . . o4/3x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
------------+-----+---------+-----------------+------------------------+------------
o3x3o .   . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3x . .   x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
. x3o3o   . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
. x3o .   x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
. x . o4/3x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
. . o3o4/3x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
------------+-----+---------+-----------------+------------------------+------------
o3x3o3o   . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3x3o .   x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3x . o4/3x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3o3o4/3x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10


o3x3o3/2o4x

. . .   . . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
------------+-----+---------+-----------------+------------------------+------------
. x .   . . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
. . .   . x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
------------+-----+---------+-----------------+------------------------+------------
o3x .   . . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
. x3o   . . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
. x .   . x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
. . .   o4x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
------------+-----+---------+-----------------+------------------------+------------
o3x3o   . . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3x .   . x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
. x3o3/2o . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
. x3o   . x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
. x .   o4x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
. . o3/2o4x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
------------+-----+---------+-----------------+------------------------+------------
o3x3o3/2o . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3x3o   . x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3x .   o4x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3o3/2o4x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10


o3x3/2o3o4x

. .   . . . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
------------+-----+---------+-----------------+------------------------+------------
. x   . . . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
. .   . . x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
------------+-----+---------+-----------------+------------------------+------------
o3x   . . . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
. x3/2o . . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
. x   . . x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
. .   . o4x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
------------+-----+---------+-----------------+------------------------+------------
o3x3/2o . . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3x   . . x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
. x3/2o3o . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
. x3/2o . x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
. x   . o4x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
. .   o3o4x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
------------+-----+---------+-----------------+------------------------+------------
o3x3/2o3o . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3x3/2o . x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3x   . o4x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3/2o3o4x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10


o3x3/2o3/2o4/3x

. .   .   .   . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
----------------+-----+---------+-----------------+------------------------+------------
. x   .   .   . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
. .   .   .   x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
----------------+-----+---------+-----------------+------------------------+------------
o3x   .   .   . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
. x3/2o   .   . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
. x   .   .   x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
. .   .   o4/3x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
----------------+-----+---------+-----------------+------------------------+------------
o3x3/2o   .   . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3x   .   .   x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
. x3/2o3/2o   . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
. x3/2o   .   x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
. x   .   o4/3x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
. .   o3/2o4/3x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
----------------+-----+---------+-----------------+------------------------+------------
o3x3/2o3/2o   . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3x3/2o   .   x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3x   .   o4/3x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3/2o3/2o4/3x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10


o3/2x3o3o4/3x

.   . . .   . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
--------------+-----+---------+-----------------+------------------------+------------
.   x . .   . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
.   . . .   x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x . .   . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
.   x3o .   . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
.   x . .   x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
.   . . o4/3x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x3o .   . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3/2x . .   x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
.   x3o3o   . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
.   x3o .   x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
.   x . o4/3x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
.   . o3o4/3x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x3o3o   . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3/2x3o .   x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3/2x . o4/3x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
.   x3o3o4/3x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10


o3/2x3o3/2o4x

.   . .   . . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
--------------+-----+---------+-----------------+------------------------+------------
.   x .   . . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
.   . .   . x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x .   . . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
.   x3o   . . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
.   x .   . x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
.   . .   o4x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x3o   . . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3/2x .   . x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
.   x3o3/2o . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
.   x3o   . x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
.   x .   o4x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
.   . o3/2o4x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x3o3/2o . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3/2x3o   . x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3/2x .   o4x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
.   x3o3/2o4x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10


o3/2x3/2o3o4x

.   .   . . . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
--------------+-----+---------+-----------------+------------------------+------------
.   x   . . . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
.   .   . . x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x   . . . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
.   x3/2o . . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
.   x   . . x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
.   .   . o4x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x3/2o . . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3/2x   . . x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
.   x3/2o3o . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
.   x3/2o . x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
.   x   . o4x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
.   .   o3o4x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
--------------+-----+---------+-----------------+------------------------+------------
o3/2x3/2o3o . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3/2x3/2o . x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3/2x   . o4x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
.   x3/2o3o4x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10


o3/2x3/2o3/2o4/3x

.   .   .   .   . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
------------------+-----+---------+-----------------+------------------------+------------
.   x   .   .   . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
.   .   .   .   x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
------------------+-----+---------+-----------------+------------------------+------------
o3/2x   .   .   . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
.   x3/2o   .   . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
.   x   .   .   x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
.   .   .   o4/3x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
------------------+-----+---------+-----------------+------------------------+------------
o3/2x3/2o   .   . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3/2x   .   .   x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
.   x3/2o3/2o   . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
.   x3/2o   .   x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
.   x   .   o4/3x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
.   .   o3/2o4/3x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
------------------+-----+---------+-----------------+------------------------+------------
o3/2x3/2o3/2o   . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3/2x3/2o   .   x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3/2x   .   o4/3x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
.   x3/2o3/2o4/3x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10

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