Acronym ...
Name 2hex+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:
hex+8oct  

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


Incidence matrix according to Dynkin symbol

β3o3o4o

both( . . . . ) | 8 ♦ 24 | 12 24 |  8 6
----------------+---+----+-------+-----
sefa( β3o . . ) | 2 | 96 |  1  2 |  2 1
----------------+---+----+-------+-----
      β3o . .   ♦ 3 |  3 | 32  * |  2 0
sefa( β3o3o . ) | 3 |  3 |  * 64 |  1 1
----------------+---+----+-------+-----
      β3o3o .   ♦ 4 | 12 |  4  4 | 16 *
sefa( β3o3o4o ) ♦ 6 | 12 |  0  8 |  * 8

starting figure: x3o3o4o


β3o3o *b3o

both( . . .    . ) | 8 ♦ 24 | 12 12 12 | 4 4 6
-------------------+---+----+----------+------
sefa( β3o .    . ) | 2 | 96 |  1  1  1 | 1 1 1
-------------------+---+----+----------+------
      β3o .    .   ♦ 3 |  3 | 32  *  * | 1 1 0
sefa( β3o3o    . ) | 3 |  3 |  * 32  * | 1 0 1
sefa( β3o . *b3o ) | 3 |  3 |  *  * 32 | 0 1 1
-------------------+---+----+----------+------
      β3o3o    .   ♦ 4 | 12 |  4  4  0 | 8 * *
      β3o . *b3o   ♦ 4 | 12 |  4  0  4 | * 8 *
sefa( β3o3o *b3o ) ♦ 6 | 12 |  0  4  4 | * * 8

starting figure: x3o3o *b3o

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