Acronym | gabric |
Name | great birhombatotetracontoctachoron |
Circumradius | sqrt[a2 + 2 sqrt(2) ab + 3b2] |
Face vector | 576, 2880, 3360, 1056 |
Confer | |
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This polychoron is the general form of one of the 3 phases of the tegum sum of 2 inverted general srico variants, ao3ob4bo3oa&#zc, here in fact the realm of 2+sqrt(2) < b:a < ∞. The other ones will be sabric for 0 < b:a < 1/2 resp. mabric for 1/2 < b:a < 2+sqrt(2).
Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases b:a = 2+sqrt(2) (recont) and b:a → ∞ (bamic) respectively.
Incidence matrix according to Dynkin symbol
ao3ob4bo3oa&#zc → height = 0 c = sqrt[(2-sqrt(2)) a2 - (6-4 sqrt(2)) ab + (6-4 sqrt(2)) b2] 2+sqrt(2) < b:a < ∞ o.3o.4o.3o. & | 576 | 2 4 4 | 1 4 2 6 6 | 2 5 2 2 ------------------+-----+---------------+-----------------------+--------------- a. .. .. .. & | 2 | 576 * * | 1 2 0 2 0 | 2 2 1 0 .. .. b. .. & | 2 | * 1152 * | 0 1 1 0 1 | 1 1 0 1 oo3oo4oo3oo&#c | 2 | * * 1152 | 0 0 0 2 2 | 0 2 1 1 ------------------+-----+---------------+-----------------------+--------------- a.3o. .. .. & | 3 | 3 0 0 | 192 * * * * | 2 0 0 0 a. .. b. .. & | 4 | 2 2 0 | * 576 * * * | 1 1 0 0 .. o.4b. .. & | 4 | 0 4 0 | * * 288 * * | 1 0 0 1 ao .. .. ..&#c & | 3 | 1 0 2 | * * * 1152 * | 0 1 1 0 .. ob .. ..&#c & | 3 | 0 1 2 | * * * * 1152 | 0 1 0 1 ------------------+-----+---------------+-----------------------+--------------- a.3o.4b. .. & | 24 | 24 24 0 | 8 12 6 0 0 | 48 * * * (a,b)-sirco variant ao .. bo ..&#c & | 5 | 2 2 4 | 0 1 0 2 2 | * 576 * * (a,b,c)-squippy variant ao .. .. oa&#c | 4 | 2 0 4 | 0 0 0 4 0 | * * 288 * tetragonal disphenoid (tet variant) .. ob4bo ..&#c | 8 | 0 8 8 | 0 0 2 0 8 | * * * 144 squap variant
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