When represented as oxoo3ooxo oxoo3ooxo3ooox&#xt it becomes apparent that bril allows for a heptadiminishing
by omitting the uppermost (single) vertex plus 3 mutually orthogonally chosen vertex pairs from the octs
of the third vertex layer (B). It further becomes apparent that those 7 vertices then mutually have a pairwise distance of
q=sqrt(2), i.e. belong to a vertex-inscribed q-scaled hop.
As a mere diminishing its according all unit-edged outcome, i.e. this polypeton, clearly is a CRF,
but it further turns out that it is scaliform as well.
Each of those 7 diminishings clearly chops off a vertex figure pyramid of the starting figure,
i.e. a tratetpy.
In fact, the single tet of the fourth vertex layer (C) of the above mentioned representation of bril
will be one of the second kind in the below incidence matrix. On the other hand the 3 tets of the first vertex layer (A),
i.e. of its the tratet section (herein becoming a true facet), belong to the first kind.
The latter ones each show up a pair of opposite edges, which is not parallel to the remaining square sides of the original
2 neighbouring octs in the second vertex layer of bril.
Those edges then, together with the remaining oct-connecting edges of that troct section again
define the remaining 6 tets of the second kind.
And the edges of those 7 tets in turn are exactly the edges of the first type in the below incidence matrix.
Incidence matrix
28 | 3 6 | 3 3 9 3 12 | 3 1 15 9 18 | 6 12 6 9 | 3 3 4
---+-------+----------------+---------------+-------------+------
2 | 42 * | 2 0 2 0 2 | 1 1 6 1 4 | 2 6 3 2 | 1 2 3
2 | * 84 | 0 1 2 1 3 | 1 0 5 4 7 | 3 6 3 5 | 2 2 3
---+-------+----------------+---------------+-------------+------
3 | 3 0 | 28 * * * * | 0 1 3 0 0 | 0 3 3 0 | 0 1 3
3 | 0 3 | * 28 * * * | 0 0 3 3 0 | 0 3 3 3 | 1 1 3
3 | 1 2 | * * 84 * * | 1 0 2 0 2 | 2 4 1 1 | 1 2 2
4 | 0 4 | * * * 21 * | 0 0 0 2 4 | 2 2 1 4 | 2 1 2
4 | 1 3 | * * * * 84 | 0 0 1 1 2 | 1 2 1 2 | 1 1 2
---+-------+----------------+---------------+-------------+------
4 | 2 4 | 0 0 4 0 0 | 21 * * * * | 2 2 0 0 | 1 2 1 tet
4 | 6 0 | 4 0 0 0 0 | * 7 * * * | 0 0 3 0 | 0 0 3 tet
5 | 3 5 | 1 1 2 0 1 | * * 84 * * | 0 2 1 0 | 0 1 2 squippy
6 | 1 8 | 0 2 0 1 2 | * * * 42 * | 0 0 1 2 | 1 0 2 trip
6 | 2 7 | 0 0 2 1 2 | * * * * 84 | 1 1 0 1 | 1 1 1 trip
---+-------+----------------+---------------+-------------+------
8 | 4 12 | 0 0 8 2 4 | 2 0 0 0 4 | 21 * * * | 1 1 0 tepe
8 | 6 12 | 2 2 8 1 4 | 1 0 4 0 2 | * 42 * * | 0 1 1 bidrap
8 | 6 12 | 4 4 4 1 4 | 0 1 4 2 0 | * * 21 * | 0 0 2 bidrap
9 | 3 15 | 0 3 3 3 6 | 0 0 0 3 3 | * * * 28 | 1 0 1 triddip
---+-------+----------------+---------------+-------------+------
12 | 6 24 | 0 4 12 6 12 | 3 0 0 6 12 | 3 0 0 4 | 7 * * tratet
12 | 12 24 | 4 4 24 3 12 | 6 0 12 0 12 | 3 6 0 0 | * 7 * tedrix
16 | 18 36 | 12 12 24 6 24 | 3 3 24 12 12 | 0 6 6 4 | * * 7 teddot
