Acronym	steth
Name	small tesseractitesseractihexadecachoron
Cross sections	©
Circumradius	sqrt[(3+sqrt(2))/2] = 1.485633
Inradius wrt. tet	[1+2 sqrt(2)]/sqrt(8) = 1.353553
Inradius wrt. cube	(1+sqrt(2))/2 = 1.207107
Inradius wrt. socco	1/2 = 0.5
Coordinates	((1+sqrt(2))/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume	[19+24 sqrt(2)]/6 = 8.823521
Surface	[72+68 sqrt(2)]/3 = 56.055507
General of army	sidpith
Colonel of regiment	sidpith
Dihedral angles (at margins)	at {4} between cube and socco:   90° at {8} between socco and socco:   90° at {3} between socco and tet:   60°
Face vector	64, 192, 136, 32
Confer	general polytopal classes: Wythoffian polychora   analogs: socco series
External links

As abstract polytope steth is isomorphic to gittith, thereby replacing octagons by octagrams, resp. socco by gocco. – As such steth is a lieutenant.

Incidence matrix according to Dynkin symbol

o3o3x4x4/3*b

. . . .      | 64 |  3  3 |  3  3  3 |  1 1 3
-------------+----+-------+----------+-------
. . x .      |  2 | 96  * |  2  0  1 |  1 0 2
. . . x      |  2 |  * 96 |  0  2  1 |  0 1 2
-------------+----+-------+----------+-------
. o3x .      |  3 |  3  0 | 64  *  * |  1 0 1
. o . x4/3*b |  4 |  0  4 |  * 48  * |  0 1 1
. . x4x      |  8 |  4  4 |  *  * 24 |  0 0 2
-------------+----+-------+----------+-------
o3o3x .      ♦  4 |  6  0 |  4  0  0 | 16 * *
o3o . x4/3*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
. o3x4x4/3*b ♦ 24 | 24 24 |  8  6  6 |  * * 8

o3o3/2x4x4*b

. .   . .    | 64 |  3  3 |  3  3  3 |  1 1 3
-------------+----+-------+----------+-------
. .   x .    |  2 | 96  * |  2  0  1 |  1 0 2
. .   . x    |  2 |  * 96 |  0  2  1 |  0 1 2
-------------+----+-------+----------+-------
. o3/2x .    |  3 |  3  0 | 64  *  * |  1 0 1
. o   . x4*b |  4 |  0  4 |  * 48  * |  0 1 1
. .   x4x    |  8 |  4  4 |  *  * 24 |  0 0 2
-------------+----+-------+----------+-------
o3o3/2x .    ♦  4 |  6  0 |  4  0  0 | 16 * *
o3o   . x4*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
. o3/2x4x4*b ♦ 24 | 24 24 |  8  6  6 |  * * 8

o3/2o3x4x4/3*b

.   . . .      | 64 |  3  3 |  3  3  3 |  1 1 3
---------------+----+-------+----------+-------
.   . x .      |  2 | 96  * |  2  0  1 |  1 0 2
.   . . x      |  2 |  * 96 |  0  2  1 |  0 1 2
---------------+----+-------+----------+-------
.   o3x .      |  3 |  3  0 | 64  *  * |  1 0 1
.   o . x4/3*b |  4 |  0  4 |  * 48  * |  0 1 1
.   . x4x      |  8 |  4  4 |  *  * 24 |  0 0 2
---------------+----+-------+----------+-------
o3/2o3x .      ♦  4 |  6  0 |  4  0  0 | 16 * *
o3/2o . x4/3*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
.   o3x4x4/3*b ♦ 24 | 24 24 |  8  6  6 |  * * 8

o3/2o3/2x4x4*b

.   .   . .    | 64 |  3  3 |  3  3  3 |  1 1 3
---------------+----+-------+----------+-------
.   .   x .    |  2 | 96  * |  2  0  1 |  1 0 2
.   .   . x    |  2 |  * 96 |  0  2  1 |  0 1 2
---------------+----+-------+----------+-------
.   o3/2x .    |  3 |  3  0 | 64  *  * |  1 0 1
.   o   . x4*b |  4 |  0  4 |  * 48  * |  0 1 1
.   .   x4x    |  8 |  4  4 |  *  * 24 |  0 0 2
---------------+----+-------+----------+-------
o3/2o3/2x .    ♦  4 |  6  0 |  4  0  0 | 16 * *
o3/2o   . x4*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
.   o3/2x4x4*b ♦ 24 | 24 24 |  8  6  6 |  * * 8