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# arithmetic – Can you assemble a nonagon with 47 rods?

Stiv’s Diabolical Instruments now presents a bundle of precisely 47 equal-length rods that may be joined by hinges at their ends – and solely the ends – to kind planar linkages (i.e. all hinge axes are parallel to the airplane containing the rods and rod thickness is uncared for).

With 35 of those rods you may make a inflexible linkage containing the vertices of a daily heptagon:

Now you wish to do the identical for a daily nonagon. But the most effective identified bracing of a daily nonagon makes use of 51 rods, greater than you could have from one bundle:

Nevertheless it’s doable to kind a inflexible linkage containing the vertices of a daily nonagon utilizing solely 47 rods by imagining that you’ve 7 extra rods, making a totally symmetric ($$D_{18}$$ symmetry, similar as that of the nonagon) inflexible linkage with these 54 rods and eradicating 7 redundant rods. What does the 47-rod linkage appear to be?

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