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If you have a VRML plugin
you can see and investigate the complete polyhedron
here.
(You can check here and
find available plugins for your browser/OS.)
The polyhedron is a compound of 30 cubes and belongs to the symmetry group
30 | A_{5} x I / C_{2} x I / μ,
as described in H.F.Verheyen's Symmetry Orbits.
The angle μ uniquely identifies one compound in the group and may
vary between 0 and 45 degrees (with 0 and 45 not included).
For some angles μ the compound has some special properties.
For this compound the angle μ = acos(^{√(5+√5)}/_{√10})
and for that angle the compound can be divided into six base elements:
5 | D_{20} x I / D_{4} x I,
for which each order 20 symmetry axis shares an order 5 symmetry axis with the compound.
(In the
wrl model the base
elements have different colours.)
Also holds that each order 2 symmetry axis of the compound is shared by two
order 2 symmetry axes of two base elements.
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The model itself is built with 250 gr/m ^{2}
chromolux paper
using the colour pearl. This colour was chosen, because the model was a
wedding present for two friends of mine. I thought it was not fitting to use
another colour and I am pretty satisfied with the result. Since the model is
quite small for 30 cubes it was difficult to get all the edges straight,
though I don't think that my friends will complain... ;)
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Here are some more pictures of the model:
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- Taken into an order 2 symmetry axis.
- Taken into an order 3 symmetry axis.
- Taken into an order 5 symmetry axis.

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A complete table about cube compounds can be found here
here.
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2009-04-28, 20:45