Acronym	tho
Name	tesseractihemioctachoron, octahemioctachoron, vertex figure of hehad
Cross sections	©
Circumradius	1/sqrt(2) = 0.707107
Inradius wrt. tet	1/sqrt(8) = 0.353553
Inradius wrt. oct	0
Coordinates	in orthoplex position:   (1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign in hemitesseract position:   (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all even permutations, all even changes of sign in "the other" (mirrored) hemitesseract position:   (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), -1/sqrt(8))   & all even permutations, all even changes of sign
Surface	sqrt(8) = 2.828427
General of army	hex
Colonel of regiment	hex
Dihedral angles (at margins)	at {3} between oct and tet:   60°
Face vector	8, 24, 32, 12
Confer	Grünbaumian relatives: 2tho   2tho+24{4}   ox3/2ox3xo&#x   general polytopal classes: segmentochora   non-orientable   analogs: demicross hOn
External links

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

Incidence matrix

  8 ♦  6 | 12 | 4 3
----+----+----+----
  2 | 24 |  4 | 2 2
----+----+----+----
  3 |  3 | 32 | 1 1
----+----+----+----
♦ 4 |  6 |  4 | 8 *
♦ 6 | 12 |  8 | * 4

reduced( ox3/2ox3xo&#x, by base 2tet )

         o.3/2o.3o.                        | 4 * | 3  3 0 | 3  3  6 0 | 1 3 3 0
reduced( .o3/2.o3.o    )                   | * 4 | 0  3 3 | 0  6  3 3 | 0 3 3 1
-------------------------------------------+-----+--------+-----------+--------
         ..   .. x.                        | 2 0 | 6  * * | 2  0  2 0 | 1 1 2 0
reduced( oo3/2oo3oo&#x )                   | 1 1 | * 12 * | 0  2  2 0 | 0 2 2 0
reduced( .x   .. ..     &  ..   .x ..    ) | 0 2 | *  * 6 | 0  2  0 2 | 0 1 2 1
-------------------------------------------+-----+--------+-----------+--------
         ..   o.3x.                        | 3 0 | 3  0 0 | 4  *  * * | 1 0 1 0
reduced( ox   .. ..&#x  &  ..   ox ..&#x ) | 1 2 | 0  2 1 | * 12  * * | 0 1 1 0
         ..   .. xo&#x                     | 2 1 | 1  2 0 | *  * 12 * | 0 1 1 0
         ..   .x3.o                        | 0 3 | 0  0 3 | *  *  * 4 | 0 0 1 1
-------------------------------------------+-----+--------+-----------+--------
         o.3/2o.3x.                        ♦ 4 0 | 6  0 0 | 4  0  0 0 | 1 * * *
         ox   .. xo&#x                     ♦ 2 2 | 1  4 1 | 0  2  2 0 | * 6 * *
         ..   ox3xo&#x                     ♦ 3 3 | 3  6 3 | 1  3  3 1 | * * 4 *
reduced( .x3/2.x3.o    )                   ♦ 0 4 | 0  0 6 | 0  0  0 4 | * * * 1