Acronym	quacant
Name	quasicellated penteractitriacontiditeron
Field of sections	©
Circumradius	sqrt[7-2 sqrt(2)]/2 = 1.021221
Inradius wrt. pen	[5-sqrt(2)]/sqrt(20) = 0.801806
Inradius wrt. tepe	-[2 sqrt(2)-1]/sqrt(8) = -0.646447
Inradius wrt. tisdip	[3-sqrt(2)]/sqrt(12) = 0.457777
Inradius wrt. tes	-(sqrt(2)-1)/2 = -0.207107
Vertex figure	©
Coordinates	((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume	[355-251 sqrt(2)]/30 = 0.0010799
Surface	[150+20 sqrt(2)+60 sqrt(3)+sqrt(5)]/3 = 94.814463
Colonel of regiment	ginnont
Dihedral angles (at margins)	at cube between tes and tes:   45° at cube between tes and tisdip:   arccos(sqrt(2/3)) = 35.264390° at trip between tepe and tisdip:   30° at tet between pen and tepe:   arccos[2/sqrt(5)] = 26.565051°
Face vector	160, 640, 1040, 800, 242
Confer	general polytopal classes: Wythoffian polytera   analogs: quasiexpanded hypercube qeCn
External links

As abstract polytope quacant is isomorphic to scant, thereby just unfolding the vertex figure.

Incidence matrix according to Dynkin symbol

x3o3o3o4/3x

. . . .   . | 160 ♦   4   4 |   6  12   6 |   4  12  12  4 |  1  4  6  4  1
------------+-----+---------+-------------+----------------+---------------
x . . .   . |   2 | 320   * |   3   3   0 |   3   6   3  0 |  1  3  3  1  0
. . . .   x |   2 |   * 320 |   0   3   3 |   0   3   6  3 |  0  1  3  3  1
------------+-----+---------+-------------+----------------+---------------
x3o . .   . |   3 |   3   0 | 320   *   * |   2   2   0  0 |  1  2  1  0  0
x . . .   x |   4 |   2   2 |   * 480   * |   0   2   2  0 |  0  1  2  1  0
. . . o4/3x |   4 |   0   4 |   *   * 240 |   0   0   2  2 |  0  0  1  2  1
------------+-----+---------+-------------+----------------+---------------
x3o3o .   . ♦   4 |   6   0 |   4   0   0 | 160   *   *  * |  1  1  0  0  0
x3o . .   x ♦   6 |   6   3 |   2   3   0 |   * 320   *  * |  0  1  1  0  0
x . . o4/3x ♦   8 |   4   8 |   0   4   2 |   *   * 240  * |  0  0  1  1  0
. . o3o4/3x ♦   8 |   0  12 |   0   0   6 |   *   *   * 80 |  0  0  0   1 1
------------+-----+---------+-------------+----------------+---------------
x3o3o3o   . ♦   5 |  10   0 |  10   0   0 |   5   0   0  0 | 32  *  *  *  *
x3o3o .   x ♦   8 |  12   4 |   8   6   0 |   2   4   0  0 |  * 80  *  *  *
x3o . o4/3x ♦  12 |  12  12 |   4  12   3 |   0   4   3  0 |  *  * 80  *  *
x . o3o4/3x ♦  16 |   8  24 |   0  12  12 |   0   0   6  2 |  *  *  * 40  *
. o3o3o4/3x ♦  16 |   0  32 |   0   0  24 |   0   0   0  8 |  *  *  *  * 10