H3
Picture 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 'shell' shape. The heptagons are folded together by gluing two neighbouring edges so that a "pyramid roof" is obtained. The pyramid have an equilateral pentagonal base that isn't flat.
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). Overal the polyhedron seems to consist of three capital 'H's in 3D. The H could stand for heptagon and the 3 represents the third dimension.
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.
Last Updated
2019-10-14