Acronym ..., 10Y4-8T-0
Name parallelly oct dissected octet
 
 ©
Pattern
(fundamental domain)
     u         Vertices:
    /|\        u = vertices within lower trat plane
   / c \       o = vertices within upper trat plane
  b _o_ b      
 /_d/N\d_\     Edges:
u--/-a-\--u    a = {4}-inc. trat-edges
|\b  N  b/|    b = not {4}-inc. trat-edges
c/b  N  b\c    c = {4}-inc. lace-edges
o-_--a--_-o    d = not {4}-inc. lace-edges
 \ d\N/d /     
  b  u  b      Triangles:
   \ | /       N = betw. T and Y4
    \c/        Y = betw. Y4 and Y4
     o         T = betw. T and T
Confer
uniform relative:
octet  
related CRF honeycombs:
5Y4-4T-4P4   5Y4-4T-6P3-sq-para   5Y4-4T-6P3-sq-skew   10Y4-8T-1-alt   10Y4-8T-1-hel (r/l)   10Y4-8T-2-alt   10Y4-8T-2-hel (r/l)   10Y4-8T-3   5Y4-4T-6P3-tri-0   5Y4-4T-6P3-tri-1-alt   5Y4-4T-6P3-tri-1-hel (r/l)   5Y4-4T-6P3-tri-2-alt   5Y4-4T-6P3-tri-2-hel (r/l)   5Y4-4T-6P3-tri-3  
External
links
mcneill

This scaliform honeycomb is derived from octet by bisecting all of the octs into pairs of squippies with parallel planes.

Further it can be derived from 5Y4-4T-6P3-tri-0 by withdrawing the elongating layers of trips.

Finally it allows for gyrations at one set of parallel trat sections in steps of k×60° (k = 1, 2, 3), where for k = 1 and 2 (i.e. the true gyrations) two different staggering modes would exist: the 2-periodic alternating mode resp. the 6- resp. 3-periodic helical mode.


Incidence matrix

(N→∞) – seen perpendicular to squat

N |  8  4 | 24 4 |  8 10
--+-------+------+------
2 | 4N  * |  4 0 |  2  2  lacings:     b, d
2 |  * 2N |  4 2 |  2  4  square grid: a, c
--+-------+------+------
3 |  2  1 | 8N * |  1  1
4 |  0  4 |  * N |  0  2
--+-------+------+------
4 |  4  2 |  4 0 | 2N  *  tet
5 |  4  4 |  4 1 |  * 2N  squippy

(N→∞) – seen perpendicular to trat

N | 2  4 2  4 |  6  6 12 4 |  8 10
--+-----------+------------+------
2 | N  * *  * |  2  2  0 2 |  2  4  a
2 | * 2N *  * |  2  0  2 0 |  2  2  b
2 | *  * N  * |  0  0  4 2 |  2  4  c
2 | *  * * 2N |  0  2  2 0 |  2  2  d
--+-----------+------------+------
3 | 1  2 0  0 | 2N  *  * * |  1  1  abb-N
3 | 1  0 0  2 |  * 2N  * * |  1  1  add
3 | 0  1 1  1 |  *  * 4N * |  1  1  bcd
4 | 2  0 2  0 |  *  *  * N |  0  2  acac
--+-----------+------------+------
4 | 1  2 1  2 |  1  1  2 0 | 2N  *  tet
5 | 2  2 2  2 |  1  1  2 1 |  * 2N  squippy

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