Acronym ..., 5Y4-4T-6P3-tri-0
Name trat-elongated 10Y4-8T-0
VRML 
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Pattern
(fundamental domain of non-prismatic layers) 
     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      Prism layers:
   \ | /       N = betw. T and Y4
    \c/        Y = betw. Y4 and Y4
     o         T = betw. T and T
Confer
uniform relative:
etoh  
related CRF honeycombs:
10Y4-8T-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  
general polytopal classes:
scaliform  
External
links 		mcneill

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

Further it can be derived from 10Y4-8T-0 by introducing elongating layers of trip at one set of parallel trat sections.

Finally it allows for gyrations within the parallel trip layers 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→∞)

2N |  2  4 1  2 1 |  3  3  3  6 2 2  4 |  4  5  6
---+--------------+--------------------+---------
 2 | 2N  * *  * * |  1  1  1  0 1 1  0 |  1  2  2  a
 2 |  * 4N *  * * |  1  1  0  1 0 0  1 |  1  1  2  b
 2 |  *  * N  * * |  0  0  0  4 2 0  0 |  2  4  0  c
 2 |  *  * * 2N * |  0  0  2  2 0 0  0 |  2  2  0  d
 2 |  *  * *  * N |  0  0  0  0 0 2  4 |  0  0  6  e prism-lacing
---+--------------+--------------------+---------
 3 |  1  2 0  0 0 | 2N  *  *  * * *  * |  1  0  1  abb-T
 3 |  1  2 0  0 0 |  * 2N  *  * * *  * |  0  1  1  abb-Y
 3 |  1  0 0  2 0 |  *  * 2N  * * *  * |  1  1  0  add
 3 |  0  1 1  1 0 |  *  *  * 4N * *  * |  1  1  0  bcd
 4 |  2  0 2  0 0 |  *  *  *  * N *  * |  0  2  0  acac
 4 |  2  0 0  0 2 |  *  *  *  * * N  * |  0  0  2  aeae
 4 |  0  2 0  0 2 |  *  *  *  * * * 2N |  0  0  2  bebe
---+--------------+--------------------+---------
 4 |  1  2 1  2 0 |  1  0  1  2 0 0  0 | 2N  *  *  tet
 5 |  2  2 2  2 0 |  0  1  1  2 1 0  0 |  * 2N  *  squippy
 6 |  2  4 0  0 3 |  1  1  0  0 0 1  2 |  *  * 2N  trip-N

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