It either can be thought of as a degenerate 7D segmentotope with zero height, or as a 6D euclidean decomposition. In fact it amounts into a fold of gee, which is its hull, plus the 2 completely orthogonal decompositions thereof into 8 octetes each.

Incidence matrix according to Dynkin symbol

xo3oo4oo ox3oo4oo&#x   → height = 0
(oct || perp oct)

o.3o.4o. o.3o.4o.    & | 12 |  4  6 |  4  36 | 1 32  48 |  7  80 | 16 32 | 12
-----------------------+----+-------+--------+----------+--------+-------+---
x. .. .. .. .. ..    & |  2 | 24  * ♦  2   6 | 1 12  12 |  6  32 | 13 16 | 10
oo3oo4oo oo3oo4oo&#x   |  2 |  * 36 ♦  0   8 | 0  8  16 |  2  32 |  8 16 |  8
-----------------------+----+-------+--------+----------+--------+-------+---
x.3o. .. .. .. ..    & |  3 |  3  0 | 16   * ♦ 1  6   0 |  6  12 | 12  8 |  9
xo .. .. .. .. ..&#x & |  3 |  1  2 |  * 144 ♦ 0  2   4 |  1  12 |  5  8 |  6
-----------------------+----+-------+--------+----------+--------+-------+---
x.3o.4o. .. .. ..    & ♦  6 | 12  0 |  8   0 | 2  *   * ♦  6   0 | 12  0 |  8
xo3oo .. .. .. ..&#x & ♦  4 |  3  3 |  1   3 | * 96   * ♦  1   4 |  4  4 |  5
xo .. .. ox .. ..&#x   ♦  4 |  2  4 |  0   4 | *  * 144 ♦  0   4 |  2  4 |  4
-----------------------+----+-------+--------+----------+--------+-------+---
xo3oo4oo .. .. ..&#x & ♦  7 | 12  6 |  8  12 | 1  8   0 | 12   * |  4  0 |  4
xo3oo .. ox .. ..&#x & ♦  5 |  4  6 |  1   9 | 0  2   3 |  * 192 |  1  2 |  3
-----------------------+----+-------+--------+----------+--------+-------+---
xo3oo4oo ox .. ..&#x & ♦  8 | 13 12 |  8  30 | 1 16  12 |  2   8 | 24  * |  2
xo3oo .. ox3oo ..&#x   ♦  6 |  6  9 |  2  18 | 0  6   9 |  0   6 |  * 64 |  2
-----------------------+----+-------+--------+----------+--------+-------+---
xo3oo4oo ox3oo ..&#x & ♦  9 | 15 18 |  9  54 | 1 30  36 |  3  36 |  3  8 | 16

oo3xo3oo oo3ox3oo∓#x   → height = 0
(oct || perp oct)

o.3o.3o. o.3o.3o.    & | 12 |  4  6 | 2 2  36 | 1 16 16  48 |  7 40 40 | 16  8 16  8 | 6 6
-----------------------+----+-------+---------+-------------+----------+-------------+----
.. x. .. .. .. ..    & |  2 | 24  * ♦ 1 1   6 | 1  6  6  12 |  6 16 16 | 13  4  8  4 | 5 5
oo3oo3oo oo3oo3oo&#x   |  2 |  * 36 ♦ 0 0   8 | 0  4  4  16 |  2 16 16 |  8  4  8  4 | 4 4
-----------------------+----+-------+---------+-------------+----------+-------------+----
o.3x. .. .. .. ..    & |  3 |  3  0 | 8 *   * ♦ 1  6  0   0 |  6 12  0 | 12  4  4  0 | 5 4
.. x.3o. .. .. ..    & |  3 |  3  0 | * 8   * ♦ 1  0  6   0 |  6  0 12 | 12  0  4  4 | 4 5
.. xo .. .. .. ..&#x & |  3 |  1  2 | * * 144 ♦ 0  1  1   4 |  1  6  6 |  5  2  4  2 | 3 3
-----------------------+----+-------+---------+-------------+----------+-------------+----
o.3x.3o. .. .. ..    & ♦  6 | 12  0 | 4 4   0 | 2  *  *   * ♦  6  0  0 | 12  0  0  0 | 4 4
oo3xo .. .. .. ..&#x & ♦  4 |  3  3 | 1 0   3 | * 48  *   * ♦  1  4  0 |  4  2  2  0 | 3 2
.. xo3oo .. .. ..&#x & ♦  4 |  3  3 | 0 1   3 | *  * 48   * ♦  1  0  4 |  4  0  2  2 | 2 3
.. xo .. .. ox ..&#x   ♦  4 |  2  4 | 0 0   4 | *  *  * 144 ♦  0  2  2 |  2  1  2  1 | 2 2
-----------------------+----+-------+---------+-------------+----------+-------------+----
oo3xo3oo .. .. ..&#x & ♦  7 | 12  6 | 4 4  12 | 1  4  4   0 | 12  *  * |  4  0  0  0 | 2 2
oo3xo .. .. ox ..&#x & ♦  5 |  4  6 | 1 0   9 | 0  2  0   3 |  * 96  * |  1  1  1  0 | 2 1
.. xo3oo .. ox ..&#x & ♦  5 |  4  6 | 0 1   9 | 0  0  2   3 |  *  * 96 |  1  0  1  1 | 1 2
-----------------------+----+-------+---------+-------------+----------+-------------+----
oo3xo3oo .. ox ..&#x & ♦  8 | 13 12 | 4 4  30 | 1  8  8  12 |  2  4  4 | 24  *  *  * | 1 1
oo3xo .. oo3ox ..&#x   ♦  6 |  6  9 | 2 0  18 | 0  6  0   9 |  0  6  0 |  * 16  *  * | 2 0
oo3xo .. .. ox3oo&#x & ♦  6 |  6  9 | 1 1  18 | 0  3  3   9 |  0  3  3 |  *  * 32  * | 1 1
.. xo3oo .. ox3oo&#x   ♦  6 |  6  9 | 0 2  18 | 0  0  6   9 |  0  0  6 |  *  *  * 16 | 0 2
-----------------------+----+-------+---------+-------------+----------+-------------+----
oo3xo3oo oo3ox ..&#x & ♦  9 | 15 18 | 5 4  54 | 1 18 12  36 |  3 24 12 |  3  4  4  0 | 8 *
oo3xo3oo .. ox3oo&#x & ♦  9 | 15 18 | 4 5  54 | 1 12 18  36 |  3 12 24 |  3  0  4  4 | * 8