Acronym	tope, K-4.89
Name	truncated-octahedron prism
Segmentochoron display
Cross sections	©
Circumradius	sqrt(11)/2 = 1.658312
Coordinates	(sqrt(2), 1/sqrt(2), 0, 1/2)   & all permutations in all but last coord., all changes of sign
Volume	8 sqrt(2) = 11.313708
Dihedral angles	at {4} between cube and hip:   arccos[-1/sqrt(3)] = 125.264390° at {4} between hip and hip:   arccos(-1/3) = 109.471221° at {4} between cube and toe:   90° at {6} between hip and toe:   90°
Face vector	48, 96, 64, 16
Confer	general polytopal classes: Wythoffian polychora   segmentochora   lace simplices
External links

Incidence matrix according to Dynkin symbol

x x3x4o

. . . . | 48 |  1  1  2 |  1  2  2  1 | 2 1 1
--------+----+----------+-------------+------
x . . . |  2 | 24  *  * |  1  2  0  0 | 2 1 0
. x . . |  2 |  * 24  * |  1  0  2  0 | 2 0 1
. . x . |  2 |  *  * 48 |  0  1  1  1 | 1 1 1
--------+----+----------+-------------+------
x x . . |  4 |  2  2  0 | 12  *  *  * | 2 0 0
x . x . |  4 |  2  0  2 |  * 24  *  * | 1 1 0
. x3x . |  6 |  0  3  3 |  *  * 16  * | 1 0 1
. . x4o |  4 |  0  0  4 |  *  *  * 12 | 0 1 1
--------+----+----------+-------------+------
x x3x . ♦ 12 |  6  6  6 |  3  3  2  0 | 8 * *
x . x4o ♦  8 |  4  0  8 |  0  4  0  2 | * 6 *
. x3x4o ♦ 24 |  0 12 24 |  0  0  8  6 | * * 2

snubbed forms: x2s3s4o, s2s3s4o

x x3x4/3o

. . .   . | 48 |  1  1  2 |  1  2  2  1 | 2 1 1
----------+----+----------+-------------+------
x . .   . |  2 | 24  *  * |  1  2  0  0 | 2 1 0
. x .   . |  2 |  * 24  * |  1  0  2  0 | 2 0 1
. . x   . |  2 |  *  * 48 |  0  1  1  1 | 1 1 1
----------+----+----------+-------------+------
x x .   . |  4 |  2  2  0 | 12  *  *  * | 2 0 0
x . x   . |  4 |  2  0  2 |  * 24  *  * | 1 1 0
. x3x   . |  6 |  0  3  3 |  *  * 16  * | 1 0 1
. . x4/3o |  4 |  0  0  4 |  *  *  * 12 | 0 1 1
----------+----+----------+-------------+------
x x3x   . ♦ 12 |  6  6  6 |  3  3  2  0 | 8 * *
x . x4/3o ♦  8 |  4  0  8 |  0  4  0  2 | * 6 *
. x3x4/3o ♦ 24 |  0 12 24 |  0  0  8  6 | * * 2

x x3x3x

. . . . | 48 |  1  1  1  1 |  1  1  1 1  1 1 | 1 1 1 1
--------+----+-------------+-----------------+--------
x . . . |  2 | 24  *  *  * |  1  1  1 0  0 0 | 1 1 1 0
. x . . |  2 |  * 24  *  * |  1  0  0 1  1 0 | 1 1 0 1
. . x . |  2 |  *  * 24  * |  0  1  0 1  0 1 | 1 0 1 1
. . . x |  2 |  *  *  * 24 |  0  0  1 0  1 1 | 0 1 1 1
--------+----+-------------+-----------------+--------
x x . . |  4 |  2  2  0  0 | 12  *  * *  * * | 1 1 0 0
x . x . |  4 |  2  0  2  0 |  * 12  * *  * * | 1 0 1 0
x . . x |  4 |  2  0  0  2 |  *  * 12 *  * * | 0 1 1 0
. x3x . |  6 |  0  3  3  0 |  *  *  * 8  * * | 1 0 0 1
. x . x |  4 |  0  2  0  2 |  *  *  * * 12 * | 0 1 0 1
. . x3x |  6 |  0  0  3  3 |  *  *  * *  * 8 | 0 0 1 1
--------+----+-------------+-----------------+--------
x x3x . ♦ 12 |  6  6  6  0 |  3  3  0 2  0 0 | 4 * * *
x x . x ♦  8 |  4  4  0  4 |  2  0  2 0  2 0 | * 6 * *
x . x3x ♦ 12 |  6  0  6  6 |  0  3  3 0  0 2 | * * 4 *
. x3x3x ♦ 24 |  0 12 12 12 |  0  0  0 4  6 4 | * * * 2

snubbed forms: x2s3s3s, s2s3s3s

s2x3x4s

demi( . . . . ) | 48 |  1  1  1  1 | 1  1  1  2 1 | 1 1 2
----------------+----+-------------+--------------+------
demi( . x . . ) |  2 | 24  *  *  * | 1  1  0  0 1 | 0 1 2  x
demi( . . x . ) |  2 |  * 24  *  * | 1  0  1  1 0 | 1 1 1  x
      s 2 . s   |  2 |  *  * 24  * | 0  1  0  2 0 | 1 0 2  q
sefa( . . x4s ) |  2 |  *  *  * 24 | 0  0  1  1 1 | 1 1 1  w
----------------+----+-------------+--------------+------
demi( . x3x . ) |  6 |  3  3  0  0 | 8  *  *  * * | 0 1 1  x3x
      s2x 2 s   |  4 |  2  0  2  0 | * 12  *  * * | 0 0 2  x2q
      . . x4s   |  4 |  0  2  0  2 | *  * 12  * * | 1 1 0  x2w
sefa( s 2 x4s ) |  4 |  0  1  2  1 | *  *  * 24 * | 1 0 1  xw&#q
sefa( . x3x4s ) |  6 |  3  0  0  3 | *  *  *  * 8 | 0 1 1  x3w
----------------+----+-------------+--------------+------
      s 2 x4s   |  8 |  0  4  4  4 | 0  0  2  4 0 | 6 * *  xw wx&#q rectangular trapezobiprisms
      . x3x4s   | 24 | 12 12  0 12 | 4  0  6  0 4 | * 2 *  x3x3w toe variant
sefa( s2x3x4s ) | 12 |  6  3  6  3 | 1  3  0  3 1 | * * 8  xx3xw hexagonal podia (hip variant)

starting figure: x x3x4x
(mentioned just isogonal sizing represents mere alternation, i.e. without further rescaling back to uniformity)

xx3xx4oo&#x   → height = 1
(toe || toe)

o.3o.4o.    | 24  * |  1  2  1  0  0 | 2 1  1  2 0 0 | 1 2 1 0
.o3.o4.o    |  * 24 |  0  0  1  1  2 | 0 0  1  2 2 1 | 0 2 1 1
------------+-------+----------------+---------------+--------
x. .. ..    |  2  0 | 12  *  *  *  * | 2 0  1  0 0 0 | 1 2 0 0
.. x. ..    |  2  0 |  * 24  *  *  * | 1 1  0  1 0 0 | 1 1 1 0
oo3oo4oo&#x |  1  1 |  *  * 24  *  * | 0 0  1  2 0 0 | 0 2 1 0
.x .. ..    |  0  2 |  *  *  * 12  * | 0 0  1  0 2 0 | 0 2 0 1
.. .x ..    |  0  2 |  *  *  *  * 24 | 0 0  0  1 1 1 | 0 1 1 1
------------+-------+----------------+---------------+--------
x.3x. ..    |  6  0 |  3  3  0  0  0 | 8 *  *  * * * | 1 1 0 0
.. x.4o.    |  4  0 |  0  4  0  0  0 | * 6  *  * * * | 1 0 1 0
xx .. ..&#x |  2  2 |  1  0  2  1  0 | * * 12  * * * | 0 2 0 0
.. xx ..&#x |  2  2 |  0  1  2  0  1 | * *  * 24 * * | 0 1 1 0
.x3.x ..    |  0  6 |  0  0  0  3  3 | * *  *  * 8 * | 0 1 0 1
.. .x4.o    |  0  4 |  0  0  0  0  4 | * *  *  * * 6 | 0 0 1 1
------------+-------+----------------+---------------+--------
x.3x.4o.    ♦ 24  0 | 12 24  0  0  0 | 8 6  0  0 0 0 | 1 * * *
xx3xx ..&#x ♦  6  6 |  3  3  6  3  3 | 1 0  3  3 1 0 | * 8 * *
.. xx4oo&#x ♦  4  4 |  0  4  4  0  4 | 0 1  0  4 0 1 | * * 6 *
.x3.x4.o    ♦  0 24 |  0  0  0 12 24 | 0 0  0  0 8 6 | * * * 1

xx3xx3xx&#x   → height = 1
(toe || toe)

o.3o.4o.    | 24  * |  1  1  1  1  0  0  0 | 1 1 1  1  1  1 0 0 0 | 1 1 1 1 0
.o3.o4.o    |  * 24 |  0  0  0  1  1  1  1 | 0 0 0  1  1  1 1 1 1 | 0 1 1 1 1
------------+-------+----------------------+----------------------+----------
x. .. ..    |  2  0 | 12  *  *  *  *  *  * | 1 1 0  1  0  0 0 0 0 | 1 1 1 0 0
.. x. ..    |  2  0 |  * 12  *  *  *  *  * | 1 0 1  0  1  0 0 0 0 | 1 1 0 1 0
.. .. x.    |  2  0 |  *  * 12  *  *  *  * | 0 1 1  0  0  1 0 0 0 | 1 0 1 1 0
oo3oo3oo&#x |  1  1 |  *  *  * 24  *  *  * | 0 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x .. ..    |  0  2 |  *  *  *  * 12  *  * | 0 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.. .x ..    |  0  2 |  *  *  *  *  * 12  * | 0 0 0  0  1  0 1 0 1 | 0 1 0 1 1
.. .. .x    |  0  2 |  *  *  *  *  *  * 12 | 0 0 0  0  0  1 0 1 1 | 0 0 1 1 1
------------+-------+----------------------+----------------------+----------
x.3x. ..    |  6  0 |  3  3  0  0  0  0  0 | 4 * *  *  *  * * * * | 1 1 0 0 0
x. .. x.    |  4  0 |  2  0  2  0  0  0  0 | * 6 *  *  *  * * * * | 1 0 1 0 0
.. x.3x.    |  4  0 |  0  3  3  0  0  0  0 | * * 4  *  *  * * * * | 1 0 0 1 0
xx .. ..&#x |  2  2 |  1  0  0  2  1  0  0 | * * * 12  *  * * * * | 0 1 1 0 0
.. xx ..&#x |  2  2 |  0  1  0  2  0  1  0 | * * *  * 12  * * * * | 0 1 0 1 0
.. .. xx&#x |  2  2 |  0  0  1  2  0  0  1 | * * *  *  * 12 * * * | 0 0 1 1 0
.x3.x ..    |  0  6 |  0  0  0  0  3  3  0 | * * *  *  *  * 4 * * | 0 1 0 0 1
.x .. .x    |  0  4 |  0  0  0  0  2  0  2 | * * *  *  *  * * 6 * | 0 0 1 0 1
.. .x3.x    |  0  6 |  0  0  0  0  0  2  2 | * * *  *  *  * * * 4 | 0 0 0 1 1
------------+-------+----------------------+----------------------+----------
x.3x.3x.    ♦ 24  0 | 12 12 12  0  0  0  0 | 4 6 4  0  0  0 0 0 0 | 1 * * * *
xx3xx ..&#x ♦  6  6 |  3  3  0  6  3  3  0 | 1 0 0  3  3  0 1 0 0 | * 4 * * *
xx .. xx&#x ♦  4  4 |  2  0  2  4  2  0  2 | 0 1 0  2  0  2 0 1 0 | * * 6 * *
.. xx3xx&#x ♦  6  6 |  0  3  3  6  0  3  3 | 0 0 1  0  3  3 0 0 1 | * * * 4 *
.x3.x3.x    ♦  0 24 |  0  0  0  0 12 12 12 | 0 0 0  0  0  0 4 6 4 | * * * * 1