Acronym ..., 5Y4-4T-6P3-tri-2-hel
Name trat-elongated 10Y4-8T-2-hel
VRML 
 ⭳ ©
Pattern
(fundamental domain of non-prismatic layers) 
     u         Vertices:
    /|\        u = vertices within lower trat plane
   / c \       o = vertices within upper trat plane
  a'_o_ b      
 /_d/N\d_\     Edges:
u--/-a-\--u    a = {4}-inc. trat-edges / a' = P3-separated from a-edge of next layer
|\b  N a'/|    b = not {4}-inc. trat-edges
c/b  N a'\c    c = {4}-inc. lace-edges
o-_--a--_-o    d = not {4}-inc. lace-edges
 \ d\N/d /     
  a' u  b      Prism layers:
   \ | /       N = betw. T and Y4
    \c/        Y = betw. Y4 and Y4
     o         T = betw. T and T
Confer
related CRF honeycombs:
10Y4-8T-2-hel (r/l)   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-3  
general polytopal classes:
scaliform  
External
links 		mcneill

This scaliform honeycomb is derived from 10Y4-8T-2-hel by introducing elongating layers of trip at the parallel trat sections.

Further it occurs as gyration within the parallel trip layers of 5Y4-4T-6P3-tri-0 in steps of 2×60° using the 3-periodic helical staggering mode.

Note that this very vertex configuration shown above can be used with layer alternating (5Y4-4T-6P3-tri-2-alt) or with helical stacking (here).


Incidence matrix

(N→∞)

2N |  2  2  2 1  2 1 |  3  3  3  3  3 2  4 2 |  4  5  6
---+-----------------+-----------------------+---------
 2 | 2N  *  * *  * * |  1  1  0  0  1 1  1 0 |  1  2  2  a  inc. to skew {4}
 2 |  * 2N  * *  * * |  1  1  1  0  0 0  1 0 |  1  1  2  a' not inc. to skew {4}
 2 |  *  * 2N *  * * |  1  1  0  1  0 0  0 1 |  1  1  2  b
 2 |  *  *  * N  * * |  0  0  2  2  0 2  0 0 |  2  4  0  c
 2 |  *  *  * * 2N * |  0  0  1  1  2 0  0 0 |  2  2  0  d
 2 |  *  *  * *  * N |  0  0  0  0  0 0  4 2 |  0  0  6  e  prism-lacing
---+-----------------+-----------------------+---------
 3 |  1  1  1 0  0 0 | 2N  *  *  *  * *  * * |  1  0  1  aa'b-T
 3 |  1  1  1 0  0 0 |  * 2N  *  *  * *  * * |  0  1  1  aa'b-Y
 3 |  0  1  0 1  1 0 |  *  * 2N  *  * *  * * |  1  1  0  a'cd
 3 |  0  0  1 1  1 0 |  *  *  * 2N  * *  * * |  1  1  0  bcd
 3 |  1  0  0 0  2 0 |  *  *  *  * 2N *  * * |  1  1  0  add
 4 |  2  0  0 2  0 0 |  *  *  *  *  * N  * * |  0  2  0  acac
 4 |  1  1  0 0  0 2 |  *  *  *  *  * * 2N * |  0  0  2  aea'e
 4 |  0  0  2 0  0 2 |  *  *  *  *  * *  * N |  0  0  2  bebe
---+-----------------+-----------------------+---------
 4 |  1  1  1 1  2 0 |  1  0  1  1  1 0  0 0 | 2N  *  *  tet
 5 |  2  1  1 2  2 0 |  0  1  1  1  1 1  0 0 |  * 2N  *  squippy
 6 |  2  2  2 0  0 3 |  1  1  0  0  0 0  2 1 |  *  * 2N  trip-N

© 2004-2025
top of page