# Heptagonal Roofs

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Pictures copyright by
PhotoArt Studio HĂ¶rby
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This model was built in 2011 and its dimensions is around 11 cm x 11 cm x 11 cm.
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This polyhedron only consists of regular heptagons that are folded over a
diagonal. There are different ways in which you can fold a regular heptagon and
for this polyhedron the folding is done in a 'W' shape.
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he polyhedron has the same rotational symmetry as a tetrahedraon, however a central inversion is included to the symmetry group (which a tetrahedron doesn't have).
This model is really easy to build and since it doesn't have any intersections,
one only need to be able to draw a heptagon to build it.
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For most of the polyhedra I didn't really proof that the heptagons are really regular. For this one I did put together a proof that there should be a solution for a regular heptagon. This means that I didn't proof it by a direct algebraic calculation. Instead I showed that for heptagons this kind of polyhedron can be obtained and that there is no singularity for the regular heptagon.
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The interesting thing is that this one is closely related to
H ^{3} which has a 'shell' fold instead of a 'W'
fold.
H^{3} consists of pyramids roofs with a pentagonal base.
Such a pentagonal base is shown in the figure below.
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## Last Updated

2019-10-14