Acronym | haxesc |
Name |
(degenerate) demihexaractic scalene, line atop fully orthogonal demihexaract |
Circumradius | ∞ i.e. flat in euclidean space |
Face vector | 34, 305, 1152, 2160, 2172, 1188, 341, 46 |
The hull of this degenerate shape is haxt. In fact, the latter provides 2 different decompositions, either into 12 hinscs plus 32 ocas (kind in the sense of a 7D orange) or equatorially into 2 haxpies. The blend of these 2 decompositions, blending out right those haxt cells each, then would result in haxesc again.
In fact, it is only this degeneracy, which lets become here the hull of a scalene to be a mere bipyramid.
Incidence matrix according to Dynkin symbol
xo ox3oo3oo *c3oo3oo3oo&#x → height = 0 (pyramid product of line with hax) o. o.3o.3o. *c3o.3o.3o. | 2 * ♦ 1 32 0 | 32 240 0 | 240 640 0 0 | 640 160 480 0 0 | 160 480 60 192 0 0 | 60 192 12 32 0 | 12 32 1 .o .o3.o3.o *c3.o3.o3.o | * 32 ♦ 0 2 15 | 1 30 60 | 15 120 20 60 | 60 40 120 15 30 | 20 60 30 60 6 6 | 15 30 12 12 1 | 6 6 2 ---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+-------- x. .. .. .. .. .. .. | 2 0 | 1 * * ♦ 32 0 0 | 240 0 0 0 | 640 0 0 0 0 | 160 480 0 0 0 0 | 60 192 0 0 0 | 12 32 0 oo oo3oo3oo *c3oo3oo3oo&#x | 1 1 | * 64 * ♦ 1 15 0 | 15 60 0 0 | 60 20 60 0 0 | 20 60 15 30 0 0 | 15 30 6 6 0 | 6 6 1 .. .x .. .. .. .. .. | 0 2 | * * 240 ♦ 0 2 8 | 1 16 4 12 | 8 8 24 6 8 | 4 12 12 16 4 2 | 6 8 8 4 1 | 4 2 2 ---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+-------- xo .. .. .. .. .. ..&#x | 2 1 | 1 2 0 | 32 * * ♦ 15 0 0 0 | 60 0 0 0 0 | 20 60 0 0 0 0 | 15 30 0 0 0 | 6 6 0 .. ox .. .. .. .. ..&#x | 1 2 | 0 2 1 | * 480 * ♦ 1 8 0 0 | 8 4 12 0 0 | 4 12 6 8 0 0 | 6 8 4 2 0 | 4 2 1 .. .x3.o .. .. .. .. | 0 3 | 0 0 3 | * * 640 | 0 2 1 3 | 1 2 6 3 3 | 1 3 6 6 3 1 | 3 3 6 2 1 | 3 1 2 ---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+-------- xo ox .. .. .. .. ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 240 * * * ♦ 8 0 0 0 0 | 4 12 0 0 0 0 | 6 8 0 0 0 | 4 2 0 .. ox3oo .. .. .. ..&#x ♦ 1 3 | 0 3 3 | 0 3 1 | * 1280 * * | 1 1 3 0 0 | 1 3 3 3 0 0 | 3 3 3 1 0 | 3 1 1 .. .x3.o3.o .. .. .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * 160 * | 0 2 0 3 0 | 1 0 6 0 3 0 | 3 0 6 0 1 | 3 0 2 .. .x3.o .. *c3.o .. .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * * 480 | 0 0 2 1 2 | 0 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 ---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+-------- xo ox3oo .. .. .. ..&#x ♦ 2 3 | 1 6 3 | 3 6 1 | 3 2 0 0 | 640 * * * * | 1 3 0 0 0 0 | 3 3 0 0 0 | 3 1 0 .. ox3oo3oo .. .. ..&#x ♦ 1 4 | 0 4 6 | 0 6 4 | 0 4 1 0 | * 320 * * * | 1 0 3 0 0 0 | 3 0 3 0 0 | 3 0 1 .. ox3oo .. *c3oo .. ..&#x ♦ 1 4 | 0 4 6 | 0 6 4 | 0 4 0 1 | * * 960 * * | 0 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 .. .x3.o3.o *c3.o .. .. ♦ 0 8 | 0 0 24 | 0 0 32 | 0 0 8 8 | * * * 60 * | 0 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 .. .x3.o .. *c3.o3.o .. ♦ 0 5 | 0 0 10 | 0 0 10 | 0 0 0 5 | * * * * 192 | 0 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 ---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+-------- xo ox3oo3oo .. .. ..&#x ♦ 2 4 | 1 8 6 | 4 12 4 | 6 8 1 0 | 4 2 0 0 0 | 160 * * * * * | 3 0 0 0 0 | 3 0 0 xo ox3oo .. *c3oo .. ..&#x ♦ 2 4 | 1 8 6 | 4 12 4 | 6 8 0 1 | 4 0 2 0 0 | * 480 * * * * | 1 2 0 0 0 | 2 1 0 .. ox3oo3oo *c3oo .. ..&#x ♦ 1 8 | 0 8 24 | 0 24 32 | 0 32 8 8 | 0 8 8 1 0 | * * 120 * * * | 1 0 2 0 0 | 2 0 1 .. ox3oo .. *c3oo3oo ..&#x ♦ 1 5 | 0 5 10 | 0 10 10 | 0 10 0 5 | 0 0 5 0 1 | * * * 384 * * | 0 1 1 1 0 | 1 1 1 .. .x3.o3.o *c3.o3.o .. ♦ 0 16 | 0 0 80 | 0 0 160 | 0 0 40 80 | 0 0 0 10 16 | * * * * 12 * | 0 0 2 0 1 | 1 0 2 .. .x3.o .. *c3.o3.o3.o ♦ 0 6 | 0 0 15 | 0 0 20 | 0 0 0 15 | 0 0 0 0 6 | * * * * * 32 | 0 0 0 2 1 | 0 1 2 ---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+-------- xo ox3oo3oo *c3oo .. ..&#x ♦ 2 8 | 1 16 24 | 8 48 32 | 24 64 8 8 | 32 16 16 1 0 | 8 8 2 0 0 0 | 60 * * * * | 2 0 0 xo ox3oo .. *c3oo3oo ..&#x ♦ 2 5 | 1 10 10 | 5 20 10 | 10 20 0 5 | 10 0 10 0 1 | 0 5 0 2 0 0 | * 192 * * * | 1 1 0 .. ox3oo3oo *c3oo3oo ..&#x ♦ 1 16 | 0 16 80 | 0 80 160 | 0 160 40 80 | 0 40 80 10 16 | 0 0 10 16 1 0 | * * 24 * * | 1 0 1 .. ox3oo .. *c3oo3oo3oo&#x ♦ 1 6 | 0 6 15 | 0 15 20 | 0 20 0 15 | 0 0 15 0 6 | 0 0 0 6 0 1 | * * * 64 * | 0 1 1 .. .x3.o3.o *c3.o3.o3.o ♦ 0 32 | 0 0 240 | 0 0 640 | 0 0 160 480 | 0 0 0 60 192 | 0 0 0 0 12 32 | * * * * 1 | 0 0 2 ---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+-------- xo ox3oo3oo *c3oo3oo ..&#x ♦ 2 16 | 1 32 80 | 16 160 160 | 80 320 40 80 | 160 80 160 10 16 | 40 80 20 32 1 0 | 10 16 2 0 0 | 12 * * xo ox3oo .. *c3oo3oo3oo&#x ♦ 2 6 | 1 12 15 | 6 30 20 | 15 40 0 15 | 20 0 30 0 6 | 0 15 0 12 0 1 | 0 6 0 2 0 | * 32 * .. ox3oo3oo *c3oo3oo3oo&#x ♦ 1 32 | 0 32 240 | 0 240 640 | 0 640 160 480 | 0 160 480 60 192 | 0 0 60 192 12 32 | 0 0 12 32 1 | * * 2
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