Acronym bimteth
Name bimesotruncatotetrahedral honeycomb
Confer
general polytopal classes:
isogonal  
External
links
polytopewiki  

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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