# An Inverted Star of Heptagons with A4xI Symmetry

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This model was built in 2011 and its dimensions is around 25 cm x 25 cm x 25 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. Together with the
'W' fold these seem to give the best results of polyhedra with regulare folded
heptagons.
Here, by gluing two neighbouring
edges together, the heptagons are folded into a roof of a pyramid with one side
pushed inside.
These are positioned on a base poyhedron, but instead of pointing towards the
outside they point inwards; so much that they stick out on the other side.
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The 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).
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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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If you compare the paper model with the model in the 3D player on the right, you
should be able to see that I actually cheated a bit. I left out some small
parts. These weren't essential and would have become very small. It is hard to
see from the paper model only that some parts are missing.
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## Last Updated

2019-10-13