| Acronym | gedak |
| Name |
hexacontitetradishexeract, compound of 2 hax |
| Circumradius | sqrt(3)/2 = 0.866025 |
|
Inradius wrt. hix | 1/sqrt(3) = 0.577350 |
|
Inradius wrt. hin | 1/sqrt(8) = 0.353553 |
| General of army | ax |
| Colonel of regiment | (is itself locally convex) |
| Admiral of fleet | brox |
| Confer |
Comes in 4 types, depending on the pairs of co-realmic hin (in gyrated positioning): being counted separately (type A) or being combined to todin compounds as well. Within the latter case further depending on the pairs of co-realmic hex (in dual positioning): being counted separately (type B) or being combined to haddet compounds as well. Within the latter case further depending on the pairs of co-realmic tet (in dual positioning): being counted separately (type C) or being combined to so compounds as well (type D).
Incidence matrix according to Dynkin symbol
xo3oo3ox *b3oo3oo3oo (Type A) o.3o.3o. *b3o.3o.3o. & | 64 ♦ 15 | 60 | 20 60 | 15 30 | 6 6 || 1 ------------------------+----+-----+------+---------+---------+-------++-- x. .. .. .. .. .. & | 2 | 480 ♦ 8 | 4 12 | 6 8 | 4 2 || 1 ------------------------+----+-----+------+---------+---------+-------++-- x.3o. .. .. .. .. & | 3 | 3 | 1280 | 1 3 | 3 3 | 3 1 || 1 ------------------------+----+-----+------+---------+---------+-------++-- x.3o.3o. .. .. .. & ♦ 4 | 6 | 4 | 320 * | 3 0 | 3 0 || 1 x.3o. .. *b3o. .. .. & ♦ 4 | 6 | 4 | * 960 | 1 2 | 2 1 || 1 ------------------------+----+-----+------+---------+---------+-------++-- x.3o.3o. *b3o. .. .. & ♦ 8 | 24 | 32 | 8 8 | 120 * | 2 0 || 1 x.3o. .. *b3o.3o. .. & ♦ 5 | 10 | 10 | 0 5 | * 384 | 1 1 || 1 ------------------------+----+-----+------+---------+---------+-------++-- x.3o.3o. *b3o.3o. .. & ♦ 16 | 80 | 160 | 40 80 | 10 16 | 24 * || 1 x.3o. .. *b3o.3o.3o. & ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 64 || 1 ------------------------+----+-----+------+---------+---------+-------++-- x.3o.3o. *b3o.3o.3o. & ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 || 2
o3o3o3o3o4β (Type A) both( . . . . . . ) | 64 ♦ 15 | 60 | 20 60 | 15 30 | 6 6 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . . o4s ) | 2 | 480 ♦ 8 | 4 12 | 6 8 | 4 2 || 1 --------------------+----+-----+------+---------+---------+-------++-- sefa( . . . o3o4s ) | 3 | 3 | 1280 | 1 3 | 3 3 | 3 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . o3o4s ) ♦ 4 | 6 | 4 | 320 * | 3 0 | 3 0 || 1 sefa( . . o3o3o4s ) ♦ 4 | 6 | 4 | * 960 | 1 2 | 2 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . o3o3o4s ) ♦ 8 | 24 | 32 | 8 8 | 120 * | 2 0 || 1 sefa( . o3o3o3o4s ) ♦ 5 | 10 | 10 | 0 5 | * 384 | 1 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . o3o3o3o4s ) ♦ 16 | 80 | 160 | 40 80 | 10 16 | 24 * || 1 sefa( o3o3o3o3o4s ) ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 64 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( o3o3o3o3o4s ) ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 || 2 starting figure: o3o3o3o3o4x
o3o3o3o3o4β (Type B) both( . . . . . . ) | 64 ♦ 15 | 60 | 20 60 | 15 30 | 6 6 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . . o4s ) | 2 | 480 ♦ 8 | 4 12 | 6 8 | 4 2 || 1 --------------------+----+-----+------+---------+---------+-------++-- sefa( . . . o3o4s ) | 3 | 3 | 1280 | 1 3 | 3 3 | 3 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . o3o4s ) ♦ 4 | 6 | 4 | 320 * | 3 0 | 3 0 || 1 sefa( . . o3o3o4s ) ♦ 4 | 6 | 4 | * 960 | 1 2 | 2 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . o3o3o4s ) ♦ 8 | 24 | 32 | 8 8 | 120 * | 2 0 || 1 sefa( . o3o3o3o4s ) ♦ 5 | 10 | 10 | 0 5 | * 384 | 1 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . o3o3o3o4s ) ♦ 32 | 160 | 320 | 80 160 | 20 32 | 12 * || 2 sefa( o3o3o3o3o4s ) ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 64 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( o3o3o3o3o4s ) ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 || 2 starting figure: o3o3o3o3o4x
o3o3o3o3o4β (Type C) both( . . . . . . ) | 64 ♦ 15 | 60 | 20 60 | 15 30 | 6 6 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . . o4s ) | 2 | 480 ♦ 8 | 4 12 | 6 8 | 4 2 || 1 --------------------+----+-----+------+---------+---------+-------++-- sefa( . . . o3o4s ) | 3 | 3 | 1280 | 1 3 | 3 3 | 3 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . o3o4s ) ♦ 4 | 6 | 4 | 320 * | 3 0 | 3 0 || 1 sefa( . . o3o3o4s ) ♦ 4 | 6 | 4 | * 960 | 1 2 | 2 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . o3o3o4s ) ♦ 16 | 48 | 64 | 16 16 | 60 * | 2 0 || 2 sefa( . o3o3o3o4s ) ♦ 5 | 10 | 10 | 0 5 | * 384 | 1 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . o3o3o3o4s ) ♦ 32 | 160 | 320 | 80 160 | 20 32 | 12 * || 2 sefa( o3o3o3o3o4s ) ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 64 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( o3o3o3o3o4s ) ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 || 2 starting figure: o3o3o3o3o4x
o3o3o3o3o4β (Type D) both( . . . . . . ) | 64 ♦ 15 | 60 | 20 60 | 15 30 | 6 6 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . . o4s ) | 2 | 480 ♦ 8 | 4 12 | 6 8 | 4 2 || 1 --------------------+----+-----+------+---------+---------+-------++-- sefa( . . . o3o4s ) | 3 | 3 | 1280 | 1 3 | 3 3 | 3 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . . o3o4s ) ♦ 8 | 12 | 8 | 160 * | 3 0 | 3 0 || 2 sefa( . . o3o3o4s ) ♦ 4 | 6 | 4 | * 960 | 1 2 | 2 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . . o3o3o4s ) ♦ 16 | 48 | 64 | 16 16 | 60 * | 2 0 || 2 sefa( . o3o3o3o4s ) ♦ 5 | 10 | 10 | 0 5 | * 384 | 1 1 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( . o3o3o3o4s ) ♦ 32 | 160 | 320 | 80 160 | 20 32 | 12 * || 2 sefa( o3o3o3o3o4s ) ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 64 || 1 --------------------+----+-----+------+---------+---------+-------++-- both( o3o3o3o3o4s ) ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 || 2 starting figure: o3o3o3o3o4x
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