Rectified Polyhedra

For general discussion of polyhedra, not necessarily Stella-specific.
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Pauly1060
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Rectified Polyhedra

Post by Pauly1060 » Mon May 20, 2013 11:02 pm

I have great stella and would like to make rectified polyhedra from a parent polyhedron, twisting the pentagon faces of a dodecahedron for example, so that they are point to point instead of back to back and adding an additional triangle face to make an icosidodecahedron. Do I have to do this with truncation or is there a rectification button?

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robertw
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Re: Rectified Polyhedra

Post by robertw » Tue May 21, 2013 1:54 pm

There's no specific button for it in 3D, although in 4D you can use "4D->Rectify". Rectification is only really possible when a polyhedron has a midsphere, otherwise you have to do something that isn't quite rectification. But yes you can do it easily enough by going to the Morph Duals by Truncation view, jumping to 50% (Ctrl+Right-click, if not already at 50%), then making this the new base model with the left-and-down button at the top of that view.

By the way, after rectifying a dodecahedron, the pentagons have effectively rotated with respect to where they started, but opposite ones are still not aligned (since they both rotated).

Pauly1060
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Ah so you can't rectify any polyhedron

Post by Pauly1060 » Thu May 23, 2013 9:52 pm

Thanks for the reply, I think I found out where I was going wrong. I do use the 50% truncation method but was struggling with some models. By mid-sphere do you mean mid points of faces are the same distance from the centre.

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robertw
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Post by robertw » Thu May 23, 2013 11:56 pm

The midsphere is the one that just touches each edge. That is the edges are tangent to it. I presume it's called the midsphere because it lies somewhere between the circumsphere which touches the vertices and the insphere which the facial planes are tangent to.

The points where edges touch the midsphere become new vertices after rectification.

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