hex+8oct

Acronym	...
Name	hex+8oct (?)
Circumradius	1/sqrt(2) = 0.707107
Coordinates	as orthoplex (tetracross): (1/sqrt(2), 0, 0, 0) & all permutations, all changes of sign as hemitesseract: (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8)) & all permutations, all even changes of sign as "the other" (mirrored) hemitesseract: (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), -1/sqrt(8)) & all permutations, all even changes of sign (the compound of those 3 such oriented hexadecachora is sico, vertex inscribed in the dual ico of the intersection kernel)
General of army	hex
Colonel of regiment	hex
Confer	non-Grünbaumian master: hex Grünbaumian relatives: 2hex+8oct general polytopal classes: Wythoffian polychora

Looks like a compound of an hexadecachoron (hex) with 8 pairwise coincident diametral octahedra (oct).

Incidence matrix according to Dynkin symbol

x3o3o4o4/3*b

. . . .      | 8 ♦  6 | 24 |  8 6
-------------+---+----+----+-----
x . . .      | 2 | 24 |  8 |  4 4
-------------+---+----+----+-----
x3o . .      | 3 |  3 | 64 |  1 1
-------------+---+----+----+-----
x3o3o .      ♦ 4 |  6 |  4 | 16 *
x3o . o4/3*b ♦ 6 | 12 |  8 |  * 8

x3o3o4/3o4*b

. . .   .    | 8 ♦  6 | 24 |  8 6
-------------+---+----+----+-----
x . .   .    | 2 | 24 |  8 |  4 4
-------------+---+----+----+-----
x3o .   .    | 3 |  3 | 64 |  1 1
-------------+---+----+----+-----
x3o3o   .    ♦ 4 |  6 |  4 | 16 *
x3o .   o4*b ♦ 6 | 12 |  8 |  * 8

x3o3/2o4o4*b

. .   . .    | 8 ♦  6 | 24 |  8 6
-------------+---+----+----+-----
x .   . .    | 2 | 24 |  8 |  4 4
-------------+---+----+----+-----
x3o   . .    | 3 |  3 | 64 |  1 1
-------------+---+----+----+-----
x3o3/2o .    ♦ 4 |  6 |  4 | 16 *
x3o   . o4*b ♦ 6 | 12 |  8 |  * 8

x3o3/2o4/3o4/3*b

. .   .   .      | 8 ♦  6 | 24 |  8 6
-----------------+---+----+----+-----
x .   .   .      | 2 | 24 |  8 |  4 4
-----------------+---+----+----+-----
x3o   .   .      | 3 |  3 | 64 |  1 1
-----------------+---+----+----+-----
x3o3/2o   .      ♦ 4 |  6 |  4 | 16 *
x3o   .   o4/3*b ♦ 6 | 12 |  8 |  * 8

x3/2o3o4o4/3*b

.   . . .      | 8 ♦  6 | 24 |  8 6
---------------+---+----+----+-----
x   . . .      | 2 | 24 |  8 |  4 4
---------------+---+----+----+-----
x3/2o . .      | 3 |  3 | 64 |  1 1
---------------+---+----+----+-----
x3/2o3o .      ♦ 4 |  6 |  4 | 16 *
x3/2o . o4/3*b ♦ 6 | 12 |  8 |  * 8

x3/2o3o4/3o4*b

.   . .   .    | 8 ♦  6 | 24 |  8 6
---------------+---+----+----+-----
x   . .   .    | 2 | 24 |  8 |  4 4
---------------+---+----+----+-----
x3/2o .   .    | 3 |  3 | 64 |  1 1
---------------+---+----+----+-----
x3/2o3o   .    ♦ 4 |  6 |  4 | 16 *
x3/2o .   o4*b ♦ 6 | 12 |  8 |  * 8

x3/2o3/2o4o4*b

.   .   . .    | 8 ♦  6 | 24 |  8 6
---------------+---+----+----+-----
x   .   . .    | 2 | 24 |  8 |  4 4
---------------+---+----+----+-----
x3/2o   . .    | 3 |  3 | 64 |  1 1
---------------+---+----+----+-----
x3/2o3/2o .    ♦ 4 |  6 |  4 | 16 *
x3/2o   . o4*b ♦ 6 | 12 |  8 |  * 8

x3/2o3/2o4/3o4/3*b

.   .   .   .      | 8 ♦  6 | 24 |  8 6
-------------------+---+----+----+-----
x   .   .   .      | 2 | 24 |  8 |  4 4
-------------------+---+----+----+-----
x3/2o   .   .      | 3 |  3 | 64 |  1 1
-------------------+---+----+----+-----
x3/2o3/2o   .      ♦ 4 |  6 |  4 | 16 *
x3/2o   .   o4/3*b ♦ 6 | 12 |  8 |  * 8

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