Hinged 32 x 28 Hexagon

partcount-segment-11 partcount-total-66 shape-polygon-6 size-32s-28s-5p

Brick 1 x 1 Brick 1 x 4 Brick 1 x 6 Hinge Brick 1 x 4 Lower Hinge Brick 1 x 4 Upper Plate 1 x 3 Plate 1 x 6 Plate 2 x 16

Because MATHS

Tim Gould ( 2013-11-26, flickr.com )

26/15 is a very accurate (under 0.1%) approximation for sqrt(3). So hooray for maths. Also… with a side-length S you can make: equilateral tri – S=15 hexagon – S=15 septagon – S=21 octagon – S=12 nonagon – S=6 decagon – S=13