Acronym | gobath |
Name | great biambotetrahedral honeycomb |
Confer |
This honeycomb is the general form of one of the 2 phases of the tegum sum of 2 inverted general rich variants, ao3ob3bo3oa3*a&#zc, here in fact the realm of 3 < b:a < ∞. The other one will be sobath for 1 ≤ b:a < 3.
Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases case b:a = 3 and case b:a → ∞.
Incidence matrix according to Dynkin symbol
ao3ob3bo3oa3*a&#zc (N → ∞) →height = 0 c = sqrt[(3a2-2ab+3b2)/8] 3 < b:a < ∞ (a ≤ b without loss of generality) (tegum sum of 2 inverted (a,b)-richs) o.3o.3o.3o.3*a & | 6N | 4 4 4 | 2 4 2 2 6 6 | 2 1 5 2 2 ---------------------+----+-------------+---------------------+------------- a. .. .. .. & | 2 | 12N * * | 1 1 1 0 1 0 | 1 1 1 1 0 .. .. b. .. & | 2 | * 12N * | 0 1 0 1 0 1 | 1 0 1 0 1 oo3oo3oo3oo3*a&#c | 2 | * * 12N | 0 0 0 0 2 2 | 0 0 2 1 1 ---------------------+----+-------------+---------------------+------------- a.3o. .. .. & | 3 | 3 0 0 | 4N * * * * * | 1 1 0 0 0 a. .. b. .. & | 4 | 2 2 0 | * 6N * * * * | 1 0 1 0 0 a. .. .. o.3*a & | 3 | 3 0 0 | * * 4N * * * | 0 1 0 1 0 .. o.3b. .. & | 3 | 0 3 0 | * * * 4N * * | 1 0 0 0 1 ao .. .. .. &#c & | 3 | 1 0 2 | * * * * 12N * | 0 0 1 1 0 .. ob .. .. &#c & | 3 | 0 1 2 | * * * * * 12N | 0 0 1 0 1 ---------------------+----+-------------+---------------------+------------- a.3o.3b. .. & | 12 | 12 12 0 | 4 6 0 4 0 0 | N * * * * (a,b)-co a.3o. .. o.3*a & | 6 | 12 0 0 | 4 0 4 0 0 0 | * N * * * a-oct ao .. bo .. &#c & | 5 | 2 2 4 | 0 1 0 0 2 2 | * * 6N * * (a,b,c)-squippy ao .. .. oa3*a&#c | 6 | 6 0 6 | 0 0 2 0 6 0 | * * * 2N * tall (a,c)-trap .. ob3bo .. &#c | 6 | 0 6 6 | 0 0 0 2 0 6 | * * * * 2N shallow (b,c)-trap
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