Acronym quarn
Name quasirhombated penteract
Circumradius [3-sqrt(2)]/2 = 0.792893
Inradius
wrt. qrit
(sqrt(2)-1)/2 = 0.207107
Inradius
wrt. rap
sqrt[(43-30 sqrt(2))/20] = 0.169351
Inradius
wrt. tepe
sqrt[(17-12 sqrt(2))/8] = 0.0606602
Coordinates ((sqrt(2)-1)/2, (sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume [1205-843 sqrt(2)]/30 = 0.427266
Colonel of regiment wavinant
Dihedral angles
(at margins)
Face vector 320, 1280, 1520, 680, 122
Confer
general polytopal classes:
Wythoffian polytera  
analogs:
quasirhombated hypercube qrbCn  
External
links
polytopewiki  

As abstract polytope quarn is isomorphic to sirn, thereby replacing querco by sirco and qrit by srit. – As such quarn is a lieutenant.


Incidence matrix according to Dynkin symbol

o3o3x3o4/3x

. . . .   . | 320 |   6   2 |   6   3   6  1 |   2   3   6  3 |  1  2  3
------------+-----+---------+----------------+----------------+---------
. . x .   . |   2 | 960   * |   2   1   1  0 |   1   2   2  1 |  1  1  2
. . . .   x |   2 |   * 320 |   0   0   3  1 |   0   0   3  3 |  0  1  3
------------+-----+---------+----------------+----------------+---------
. o3x .   . |   3 |   3   0 | 640   *   *  * |   1   1   1  0 |  1  1  1
. . x3o   . |   3 |   3   0 |   * 320   *  * |   0   2   0  1 |  1  0  2
. . x .   x |   4 |   2   2 |   *   * 480  * |   0   0   2  1 |  0  1  2
. . . o4/3x |   4 |   0   4 |   *   *   * 80 |   0   0   0  3 |  0  0  3
------------+-----+---------+----------------+----------------+---------
o3o3x .   .    4 |   6   0 |   4   0   0  0 | 160   *   *  * |  1  1  0
. o3x3o   .    6 |  12   0 |   4   4   0  0 |   * 160   *  * |  1  0  1
. o3x .   x    6 |   6   3 |   2   0   3  0 |   *   * 320  * |  0  1  1
. . x3o4/3x   24 |  24  24 |   0   8  12  6 |   *   *   * 40 |  0  0  2
------------+-----+---------+----------------+----------------+---------
o3o3x3o   .   10 |  30   0 |  20  10   0  0 |   5   5   0  0 | 32  *  *
o3o3x .   x    8 |  12   4 |   8   0   6  0 |   2   0   4  0 |  * 80  *
. o3x3o4/3x   96 | 192  96 |  64  64  96 24 |   0  16  32  8 |  *  * 10

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