Acronym	firt
Name	facetorectified tesseract
Cross sections	©
Circumradius	sqrt(3/2) = 1.224745
Inradius wrt. tet	-3/sqrt(8) = -1.060660
Inradius wrt. tut	1/sqrt(8) = 0.353553
Coordinates	(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
Volume	10/3 = 3.333333
Surface	32 sqrt(2) = 45.254834
General of army	rit
Colonel of regiment	rit
Dihedral angles (at margins)	at {3} between tet and tut:   60° at {6} between tut and tut:   60°
Face vector	32, 96, 96, 32
Confer	general polytopal classes: Wythoffian polychora   analogs: facetorectified hypercube frCn
External links

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

Firt has ohos for pseudo facets.

Incidence matrix according to Dynkin symbol

x3x3o3o3/2*a

. . . .      | 32 |  3  3 |  6  3  3 | 3 3 1 1
-------------+----+-------+----------+--------
x . . .      |  2 | 48  * |  2  2  0 | 1 2 1 0
. x . .      |  2 |  * 48 |  2  0  2 | 2 1 0 1
-------------+----+-------+----------+--------
x3x . .      |  6 |  3  3 | 32  *  * | 1 1 0 0
x . . o3/2*a |  3 |  3  0 |  * 32  * | 0 1 1 0
. x3o .      |  3 |  0  3 |  *  * 32 | 1 0 0 1
-------------+----+-------+----------+--------
x3x3o .      ♦ 12 |  6 12 |  4  0  4 | 8 * * *
x3x . o3/2*a ♦ 12 | 12  6 |  4  4  0 | * 8 * *
x . o3o3/2*a ♦  4 |  6  0 |  0  4  0 | * * 8 *
. x3o3o      ♦  4 |  0  6 |  0  0  4 | * * * 8

x3x3o3/2o3*a

. . .   .    | 32 |  3  3 |  6  3  3 | 3 3 1 1
-------------+----+-------+----------+--------
x . .   .    |  2 | 48  * |  2  2  0 | 1 2 1 0
. x .   .    |  2 |  * 48 |  2  0  2 | 2 1 0 1
-------------+----+-------+----------+--------
x3x .   .    |  6 |  3  3 | 32  *  * | 1 1 0 0
x . .   o3*a |  3 |  3  0 |  * 32  * | 0 1 1 0
. x3o   .    |  3 |  0  3 |  *  * 32 | 1 0 0 1
-------------+----+-------+----------+--------
x3x3o   .    ♦ 12 |  6 12 |  4  0  4 | 8 * * *
x3x .   o3*a ♦ 12 | 12  6 |  4  4  0 | * 8 * *
x . o3/2o3*a ♦  4 |  6  0 |  0  4  0 | * * 8 *
. x3o3/2o    ♦  4 |  0  6 |  0  0  4 | * * * 8

or
. . .   .       | 32 |  6 |  6  6 |  6  2
----------------+----+----+-------+------
x . .   .     & |  2 | 96 |  2  2 |  3  1
----------------+----+----+-------+------
x3x .   .       |  6 |  6 | 32  * |  2  0
x . .   o3*a  & |  3 |  3 |  * 64 |  1  1
----------------+----+----+-------+------
x3x3o   .     & ♦ 12 | 18 |  4  4 | 16  *
x . o3/2o3*a  & ♦  4 |  6 |  0  4 |  * 16

x3x3/2o3/2o3/2*a

. .   .   .      | 32 |  3  3 |  6  3  3 | 3 3 1 1
-----------------+----+-------+----------+--------
x .   .   .      |  2 | 48  * |  2  2  0 | 1 2 1 0
. x   .   .      |  2 |  * 48 |  2  0  2 | 2 1 0 1
-----------------+----+-------+----------+--------
x3x   .   .      |  6 |  3  3 | 32  *  * | 1 1 0 0
x .   .   o3/2*a |  3 |  3  0 |  * 32  * | 0 1 1 0
. x3/2o   .      |  3 |  0  3 |  *  * 32 | 1 0 0 1
-----------------+----+-------+----------+--------
x3x3/2o   .      ♦ 12 |  6 12 |  4  0  4 | 8 * * *
x3x   .   o3/2*a ♦ 12 | 12  6 |  4  4  0 | * 8 * *
x .   o3/2o3/2*a ♦  4 |  6  0 |  0  4  0 | * * 8 *
. x3/2o3/2o      ♦  4 |  0  6 |  0  0  4 | * * * 8

or
. .   .   .         | 32 |  6 |  6  6 |  6  2
--------------------+----+----+-------+------
x .   .   .       & |  2 | 96 |  2  2 |  3  1
--------------------+----+----+-------+------
x3x   .   .         |  6 |  6 | 32  * |  2  0
x .   .   o3/2*a  & |  3 |  3 |  * 64 |  1  1
--------------------+----+----+-------+------
x3x3/2o   .       & ♦ 12 | 18 |  4  4 | 16  *
x .   o3/2o3/2*a  & ♦  4 |  6 |  0  4 |  * 16