Acronym | bimteth |
Name | bimesotruncatotetrahedral honeycomb |
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This isogonal honeycomb cannot be made uniform, i.e. having all 3 edge types at the same size. In fact it rather describes a full range of honeycombs, the singular bordering cases are bithon for a = 0, where the tets become points only, i.e. vertices do coincide by 4 then, and the uniform batatoh at the other end for a = b, where then the edge size of c runs down to zero, so vertices will coincide by 2 then and also edges of type a would fully coincide with those of type b.
Incidence matrix according to Dynkin symbol
ab3ba3oo3oo3*a&#zc (N → ∞) → height = 0 a < b c = |a-b| sqrt(3/8) o.3o.3o.3o.3*a | 4N * | 3 3 1 0 0 | 6 3 3 3 0 0 | 3 1 6 0 0 .o3.o3.o3.o3*a | * 4N | 0 0 1 3 3 | 0 0 3 3 6 3 | 0 0 6 3 1 -------------------+-------+----------------+-------------------+----------- a. .. .. .. | 2 0 | 6N * * * * | 2 2 1 0 0 0 | 2 1 2 0 0 a .. b. .. .. | 2 0 | * 6N * * * | 2 1 0 0 0 0 | 1 0 2 0 0 b oo3oo3oo3oo3*a&#c | 1 1 | * * 4N * * | 0 0 3 3 0 0 | 0 0 6 0 0 c .b .. .. .. | 0 2 | * * * 6N * | 0 0 1 0 2 0 | 0 0 2 1 0 b .. .a .. .. | 0 2 | * * * * 6N | 0 0 0 1 2 2 | 0 0 2 2 1 a -------------------+-------+----------------+-------------------+----------- a.3b. .. .. | 6 0 | 3 3 0 0 0 | 4N * * * * * | 1 0 1 0 0 a. .. .. o.3*a | 3 0 | 3 0 0 0 0 | * 4N * * * * | 1 1 0 0 0 ab .. .. .. &#c | 2 2 | 1 0 2 1 0 | * * 6N * * * | 0 0 2 0 0 .. ba .. .. &#c | 2 2 | 0 1 2 0 1 | * * * 6N * * | 0 0 2 0 0 .b3.a .. .. | 0 6 | 0 0 0 3 3 | * * * * 4N * | 0 0 1 1 0 .. .a3.o .. | 0 3 | 0 0 0 0 3 | * * * * * 4N | 0 0 0 1 1 -------------------+-------+----------------+-------------------+----------- a.3b. .. o.3*a | 12 0 | 12 6 0 0 0 | 4 4 0 0 0 0 | N * * * * (b,a)-tut variant a. .. o.3o.3*a | 4 0 | 6 0 0 0 0 | 0 4 0 0 0 0 | * N * * * a-tet ab3ba .. .. &#c | 6 6 | 3 3 6 3 3 | 1 0 3 3 1 0 | * * 4N * * ditra .b3.a3.o .. | 0 12 | 0 0 0 6 12 | 0 0 0 0 4 4 | * * * N * (b,a)-tut variant .. .a3.o3.o | 0 4 | 0 0 0 0 6 | 0 0 0 0 0 4 | * * * * N a-tet
or o.3o.3o.3o.3*a & | 4N | 3 3 1 | 6 3 6 | 3 1 6 ---------------------+----+----------+----------+------- a. .. .. .. & | 2 | 6N * * | 2 2 1 | 2 1 2 a .. b. .. .. & | 2 | * 6N * | 2 0 1 | 1 0 2 b oo3oo3oo3oo3*a&#c | 2 | * * 2N | 0 0 6 | 0 0 6 c ---------------------+----+----------+----------+------- a.3b. .. .. & | 6 | 3 3 0 | 4N * * | 1 0 1 a. .. .. o.3*a & | 3 | 3 0 0 | * 4N * | 1 1 0 ab .. .. .. &#c & | 4 | 1 1 2 | * * 6N | 0 0 2 ---------------------+----+----------+----------+------- a.3b. .. o.3*a & | 12 | 12 6 0 | 4 4 0 | N * * (b,a)-tut variant a. .. o.3o.3*a & | 4 | 6 0 0 | 0 4 0 | * N * a-tet ab3ba .. .. &#c | 12 | 6 6 6 | 2 0 6 | * * 2N ditra
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