Heptagonal Roofs

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Pictures copyright by PhotoArt Studio Hörby

This model was built in 2011 and its dimensions is around 11 cm x 11 cm x 11 cm.

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.

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.

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.

The interesting thing is that this one is closely related to H3 which has a 'shell' fold instead of a 'W' fold. H3 consists of pyramids roofs with a pentagonal base. Such a pentagonal base is shown in the figure below.

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Teun's Polyhedra

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Last Updated

2019-10-14