Acronym	firn
Name	facetorectified penteract
Cross sections	©
Circumradius	sqrt(2) = 1.414214
Inradius wrt. pen	+/− sqrt(8/5) = 1.264911
Inradius wrt. tip	−/+ sqrt(2/5) = 0.632456
Inradius wrt. deca	0
Coordinates	(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
Volume	0
Surface	64 sqrt(5) = 143.108351
General of army	rin
Colonel of regiment	rin
Dihedral angles	at tet between pen and tip:   arccos(3/5) = 53.130102° at tut between deca and tip:   arccos(3/5) = 53.130102°
Face vector	80, 320, 480, 320, 80
Confer	general polytopal classes: Wythoffian polytera   analogs: facetorectified hypercube frCn
External links

This polychoron could also be understood as a modwrap of cytopit.

Firn has firts for pseudo facets.

Incidence matrix according to Dynkin symbol

x3x3o3o3o3/2*a

. . . . .      | 80 |   4   4 |  12   6   6 | 12 12  4  4 |  4  6  4  1  1
---------------+----+---------+-------------+-------------+---------------
x . . . .      |  2 | 160   * |   3   3   0 |  3  6  3  0 |  1  3  3  1  0
. x . . .      |  2 |   * 160 |   3   0   3 |  6  3  0  3 |  3  3  1  0  1
---------------+----+---------+-------------+-------------+---------------
x3x . . .      |  6 |   3   3 | 160   *   * |  2  2  0  0 |  1  2  1  0  0
x . . . o3/2*a |  3 |   3   0 |   * 160   * |  0  2  2  0 |  0  1  2  1  0
. x3o . .      |  3 |   0   3 |   *   * 160 |  2  0  0  2 |  2  1  0  0  1
---------------+----+---------+-------------+-------------+---------------
x3x3o . .      ♦ 12 |   6  12 |   4   0   4 | 80  *  *  * |  1  1  0  0  0
x3x . . o3/2*a ♦ 12 |  12   6 |   4   4   0 |  * 80  *  * |  0  1  1  0  0
x . . o3o3/2*a ♦  4 |   6   0 |   0   4   0 |  *  * 80  * |  0  0  1  1  0
. x3o3o .      ♦  4 |   0   6 |   0   0   4 |  *  *  * 80 |  1  0  0  0  1
---------------+----+---------+-------------+-------------+---------------
x3x3o3o .      ♦ 20 |  10  30 |  10   0  20 |  5  0  0  5 | 16  *  *  *  *
x3x3o . o3/2*a ♦ 30 |  30  30 |  20  10  10 |  5  5  0  0 |  * 16  *  *  *
x3x . o3o3/2*a ♦ 20 |  30  10 |  10  20   0 |  0  5  5  0 |  *  * 16  *  *
x . o3o3o3/2*a ♦  5 |  10   0 |   0  10   0 |  0  0  5  0 |  *  *  * 16  *
. x3o3o3o      ♦  5 |   0  10 |   0   0  10 |  0  0  0  5 |  *  *  *  * 16

or
. . . . .        | 80 |   8 |  12  12 |  24   8 |  8  6  2
-----------------+----+-----+---------+---------+---------
x . . . .      & |  2 | 320 |   3   3 |   9   3 |  4  3  1
-----------------+----+-----+---------+---------+---------
x3x . . .        |  6 |   6 | 160   * |   4   0 |  2  2  0
x . . . o3/2*a & |  3 |   3 |   * 320 |   2   2 |  2  1  1
-----------------+----+-----+---------+---------+---------
x3x3o . .      & ♦ 12 |  18 |   4   4 | 160   * |  1  1  0
x . . o3o3/2*a & ♦  4 |   6 |   0   4 |   * 160 |  1  0  1
-----------------+----+-----+---------+---------+---------
x3x3o3o .      & ♦ 20 |  40 |  10  20 |   5   5 | 32  *  *
x3x3o . o3/2*a   ♦ 30 |  60 |  20  20 |  10   0 |  * 16  *
x . o3o3o3/2*a & ♦  5 |  10 |   0  10 |   0   5 |  *  * 32

x3x3o3o3/2o3*a

. . . .   .    | 80 |   4   4 |  12   6   6 | 12 12  4  4 |  4  6  4  1  1
---------------+----+---------+-------------+-------------+---------------
x . . .   .    |  2 | 160   * |   3   3   0 |  3  6  3  0 |  1  3  3  1  0
. x . .   .    |  2 |   * 160 |   3   0   3 |  6  3  0  3 |  3  3  1  0  1
---------------+----+---------+-------------+-------------+---------------
x3x . .   .    |  6 |   3   3 | 160   *   * |  2  2  0  0 |  1  2  1  0  0
x . . .   o3*a |  3 |   3   0 |   * 160   * |  0  2  2  0 |  0  1  2  1  0
. x3o .   .    |  3 |   0   3 |   *   * 160 |  2  0  0  2 |  2  1  0  0  1
---------------+----+---------+-------------+-------------+---------------
x3x3o .   .    ♦ 12 |   6  12 |   4   0   4 | 80  *  *  * |  1  1  0  0  0
x3x . .   o3*a ♦ 12 |  12   6 |   4   4   0 |  * 80  *  * |  0  1  1  0  0
x . . o3/2o3*a ♦  4 |   6   0 |   0   4   0 |  *  * 80  * |  0  0  1  1  0
. x3o3o   .    ♦  4 |   0   6 |   0   0   4 |  *  *  * 80 |  1  0  0  0  1
---------------+----+---------+-------------+-------------+---------------
x3x3o3o   .    ♦ 20 |  10  30 |  10   0  20 |  5  0  0  5 | 16  *  *  *  *
x3x3o .   o3*a ♦ 30 |  30  30 |  20  10  10 |  5  5  0  0 |  * 16  *  *  *
x3x . o3/2o3*a ♦ 20 |  30  10 |  10  20   0 |  0  5  5  0 |  *  * 16  *  *
x . o3o3/2o3*a ♦  5 |  10   0 |   0  10   0 |  0  0  5  0 |  *  *  * 16  *
. x3o3o3/2o    ♦  5 |   0  10 |   0   0  10 |  0  0  0  5 |  *  *  *  * 16

or
. . . .   .      | 80 |   8 |  12  12 |  24   8 |  8  6  2
-----------------+----+-----+---------+---------+---------
x . . .   .    & |  2 | 320 |   3   3 |   9   3 |  4  3  1
-----------------+----+-----+---------+---------+---------
x3x . .   .      |  6 |   6 | 160   * |   4   0 |  2  2  0
x . . .   o3*a & |  3 |   3 |   * 320 |   2   2 |  2  1  1
-----------------+----+-----+---------+---------+---------
x3x3o .   .    & ♦ 12 |  18 |   4   4 | 160   * |  1  1  0
x . . o3/2o3*a & ♦  4 |   6 |   0   4 |   * 160 |  1  0  1
-----------------+----+-----+---------+---------+---------
x3x3o3o   .    & ♦ 20 |  40 |  10  20 |   5   5 | 32  *  *
x3x3o .   o3*a   ♦ 30 |  60 |  20  20 |  10   0 |  * 16  *
x . o3o3/2o3*a & ♦  5 |  10 |   0  10 |   0   5 |  *  * 32