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Helix 2
An octotetrahedric double helix of pitch 10 around a cylinder made of 25 decagonal prisms. Both structures don't fit exactly one another; because of this, the cylinder undergoes an irregular deformation, ultimately responsible for its leaning:
GEOMAG constructions: Helix 2A
Helix 2A
2218 pieces: 508 balls, 1448 rods, 2 pentagons, 260 squares (11.65 kg)
GEOMAG constructions: Helix 2A, detail
Helix 2A, detail
Both pentagons belong to a pair of pentagonal cupolas which close, and help to stabilize, the cylinder at both ends. In the following table, we give the piece quantities required for several numbers of helices and turns. We haven't counted the top ends of the helices which exceed the height of the cylinder, nor any special structure at their bases; we have counted two pentagonal cupolas, although it could be appropriate to use more for bigger sizes:
 
  helices  turns  balls  rods  pentagons  squares 
  1  1  160  395  2  110 
  1  2  300  755  2  210 
  1  3  440  1115  2  310 
  1  4  580  1475  2  410 
  2  1  200  550  2  110 
  2  2  380  1070  2  210 
  2  3  560  1590  2  310 
  2  4  740  2110  2  410 
  ...  ...  ...  ...  ...  ... 
  m  n  (100+40m)n+20  (200+160m)n+40–5m 2  100n+10 
In the previous construction, all modules in each helix are attached to the central support. However, the structure of these helices is strong enough to allow using much less support. In the following construction, for each of the turns of each of the three helices, just four of ten modules are attached to the central support, in this case a 1 × 3 × 21 parallelepiped:
GEOMAG constructions: Helix 2B, view 1
Helix 2B, view 1
2266 pieces: 524 balls, 1469 rods, 273 squares (11.91 kg)
GEOMAG constructions: Helix 2B, view 2
Helix 2B, view 2
Similarly to the previous table, in the following one we have counted just the helices and the central support structure:
 
  helices  turns  balls  rods  squares 
  1  1  148  367  143 
  1  2  280  713  273 
  1  3  412  1059  403 
  2  1  200  528  143 
  2  2  384  1040  273 
  2  3  568  1552  403 
  3  1  252  689  143 
  3  2  488  1367  273 
  3  3  724  2045  403 
  ...  ...  ...  ...  ... 
  m  n  (80+52m)n+16  (180+166m)n+26–5m  130n+13 
GEOMAG constructions: Helix 2B, view 3
Helix 2B, view 3
  • Similar helices of pitch 15 at Helix 3
  • Similar helices of pitch 18 at Helix 4