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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 
  160  395  110 
  300  755  210 
  440  1115  310 
  580  1475  410 
  200  550  110 
  380  1070  210 
  560  1590  310 
  740  2110  410 
  ...  ...  ...  ...  ...  ... 
  (100+40m)n+20  (200+160m)n+40–5m 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 
  148  367  143 
  280  713  273 
  412  1059  403 
  200  528  143 
  384  1040  273 
  568  1552  403 
  252  689  143 
  488  1367  273 
  724  2045  403 
  ...  ...  ...  ...  ... 
  (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