Acronym	odhax
Name	octadiminished hemihexeract
Circumradius	sqrt(3)/2 = 0.866025
Lace hyper city in approx. ASCII-art	o x o o o x x o o o o x o x o x o o . . . x o o o x o o o x x o o o o x o x o
Face vector	24, 132, 310, 336, 162, 28
Confer	uniform relative: hax   general polytopal classes: scaliform
External links

The hemihexeract (hax) could be given as the hull of 4 cubes. In fact it then is ((xxoo xoxo xoox oxxo oxox ooxx))&#zx. This representation makes its relation to this diminishing quite obvious: here just a single of those cubes (i.e. one representation layer) is omitted.

(Note however that there is also a different octadiminished hemihexeract as well: hexaf.)

Incidence matrix according to Dynkin symbol

((xxo xox oxx oox oxo xoo))&#zx   → all heights = 0

  o.. o.. o.. o.. o.. o..       & | 24 |  2  1  8 | 1  8 12 12  8 | 12  4  8  4 20 16 |  4 2 16 12 10 | 4  6 2
----------------------------------+----+----------+---------------+-------------------+---------------+-------
  x.. ... ... ... ... ...       & |  2 | 24  *  * | 1  4  4  0  0 | 10  2  2  0  8  0 |  4 1 12  4  0 | 4  4 0
  ... ... ... ... ... x..       & |  2 |  * 12  * | 0  0  0  8  0 |  0  0  4  4  0  8 |  0 2  0  4  8 | 0  4 2
  oo. oo. oo. oo. oo. oo.  &#x  & |  2 |  *  * 96 | 0  1  2  2  2 |  2  1  2  1  6  5 |  1 1  6  5  4 | 2  4 1
----------------------------------+----+----------+---------------+-------------------+---------------+-------
  x.. x.. ... ... ... ...       & |  4 |  4  0  0 | 6  *  *  *  * |  8  0  0  0  0  0 |  4 0  8  0  0 | 4  2 0
  xx. ... ... ... ... ...  &#x  & |  4 |  2  0  2 | * 48  *  *  * |  2  0  0  0  2  0 |  1 0  4  1  0 | 2  2 0
  ... xo. ... ... ... ...  &#x  & |  3 |  1  0  2 | *  * 96  *  * |  1  1  1  0  2  0 |  1 1  4  2  0 | 2  3 0
  ... ... ... ... ox. ...  &#x  & |  3 |  0  1  2 | *  *  * 96  * |  0  0  1  1  0  2 |  0 1  0  2  3 | 0  3 1
  ooo ooo ooo ooo ooo ooo  &#x    |  3 |  0  0  3 | *  *  *  * 64 |  0  0  0  0  3  3 |  0 0  3  3  3 | 1  3 1
----------------------------------+----+----------+---------------+-------------------+---------------+-------
  xx. xo. ... ... ... ...  &#x  & ♦  6 |  5  0  4 | 1  2  2  0  0 | 48  *  *  *  *  * |  1 0  2  0  0 | 2  1 0
  ... xo. ox. ... ... ...  &#x  & ♦  4 |  2  0  4 | 0  0  4  0  0 |  * 24  *  *  *  * |  1 1  2  0  0 | 2  2 0
  ... xo. ... ... ox. ...  &#x  & ♦  4 |  1  1  4 | 0  0  2  2  0 |  *  * 48  *  *  * |  0 1  0  2  0 | 0  3 0
  ... ... ... ... ox. xo.  &#x  & ♦  4 |  0  2  4 | 0  0  0  4  0 |  *  *  * 24  *  * |  0 1  0  0  2 | 0  2 1
  xxo ... ... ... ... ...  &#x  & ♦  5 |  2  0  6 | 0  1  2  0  2 |  *  *  *  * 96  * |  0 0  2  1  0 | 1  2 0
  ... ... ... oox ... ...  &#x  & ♦  4 |  0  1  5 | 0  0  0  2  2 |  *  *  *  *  * 96 |  0 0  0  1  2 | 0  2 1
----------------------------------+----+----------+---------------+-------------------+---------------+-------
  xx. xo. ox. ... ... ...  &#x  & ♦  8 |  8  0  8 | 2  4  8  0  0 |  4  2  0  0  0  0 | 12 *  *  *  * | 2  0 0
((... xo. ox. ... ox. xo.))&#zx & ♦  8 |  4  4 16 | 0  0 16 16  0 |  0  4  8  4  0  0 |  * 6  *  *  * | 0  2 0
  xxo xox ... ... ... ...  &#x  & ♦  8 |  6  0 12 | 1  4  8  0  4 |  2  1  0  0  4  0 |  * * 48  *  * | 1  1 0
  xxo ... ... oox ... ...  &#x  & ♦  6 |  2  1 10 | 0  1  4  4  4 |  0  0  2  0  2  2 |  * *  * 48  * | 0  2 0
  ... ... ... oox oxo ...  &#x  & ♦  5 |  0  2  8 | 0  0  0  6  4 |  0  0  0  1  0  4 |  * *  *  * 48 | 0  1 1
----------------------------------+----+----------+---------------+-------------------+---------------+-------
  xxo xox oxx ... ... ...  &#x    ♦ 12 | 12  0 24 | 3 12 24  0  8 | 12  6  0  0 12  0 |  3 0  6  0  0 | 8  * *
((xxo xox ... oox oxo ...))&#zx & ♦ 12 |  8  4 32 | 1  8 24 24 16 |  4  4 12  4 16 16 |  0 1  4  8  4 | * 12 *	prism A-(BC)
  ... ... ... oox oxo xoo  &#x    ♦  6 |  0  3 12 | 0  0  0 12  8 |  0  0  0  3  0 12 |  0 0  0  0  6 | *  * 8