#
H^{3}

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Picture 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 '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.
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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).
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.
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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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## Last Updated

2019-10-14