Acronym | gabirch |
Name | great birhombatocubic honeycomb |
Confer |
This honeycomb is the general form of one of the 3 phases of the tegum sum of 2 inverted general srich variants, ao4ob3bo4oa&#zc, here in fact the realm of 3/sqrt(2) < b:a < ∞. The other ones will be sabirch for 0 < b:a < 1/sqrt(2) resp. mabirch for 1/sqrt(2) < b:a < 3/sqrt(2).
Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases b:a = 3/sqrt(2) (rebatch) and b:a → ∞ (bamich) respectively.
Incidence matrix according to Dynkin symbol
ao4ob3bo4oa&#zc (N → ∞) → height = 0 c = sqrt[3a2-2ab sqrt(2)+2b2]/2 3/sqrt(2) < b:a < ∞ o.4o.3o.4o. & | 12N | 2 4 4 | 1 4 2 6 6 | 2 5 2 2 ------------------+-----+-------------+-------------------+------------ a. .. .. .. & | 2 | 12N * * | 1 2 0 2 0 | 2 2 1 0 .. .. b. .. & | 2 | * 24N * | 0 1 1 0 1 | 1 1 0 1 oo4oo3oo4oo&#c | 2 | * * 24N | 0 0 0 2 2 | 0 2 1 1 ------------------+-----+-------------+-------------------+------------ a.4o. .. .. & | 4 | 4 0 0 | 3N * * * * | 2 0 0 0 a. .. b. .. & | 4 | 2 2 0 | * 12N * * * | 1 1 0 0 .. o.3b. .. & | 3 | 0 3 0 | * * 8N * * | 1 0 0 1 ao .. .. ..&#c & | 3 | 1 0 2 | * * * 24N * | 0 1 1 0 .. ob .. ..&#c & | 3 | 0 1 2 | * * * * 24N | 0 1 0 1 ------------------+-----+-------------+-------------------+------------ a.4o.3b. .. & | 24 | 24 24 0 | 6 12 8 0 0 | N * * * rhombicuboctahedron (sirco variant) ao .. bo ..&#c & | 5 | 2 2 4 | 0 1 0 2 2 | * 12N * * rectangular pyramid (squippy variant) ao .. .. oa&#c | 4 | 2 0 4 | 0 0 0 4 0 | * * 6N * tetragonal disphenoid (tet variant) .. ob3bo ..&#c | 6 | 0 6 6 | 0 0 2 0 6 | * * * 4N triangular antiprism (oct variant)
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