Rectified {6,3,4}

Rectified {6,3,4}

John Baez made a post this morning about the regular {6,3,4}, so let's look at the rectified {6,3,4} for today.  I love reading other's descriptions because it helps me look at things differently than I do on my own.  Here is John's post:

https://plus.google.com/117663015413546257905/posts/BUGkT3k5GKD

Like the {6,3,3} from yesterday, this is another honeycomb with hexagonal tilings for cells, but now the vertex figure is an octahedron.  

The rectification is also similar because we get trihexagonal tiling cells again.  The main difference is that those cells are interspersed with octahedra instead of tetrahedra.

The vertex figure of the rectified {6,3,4} is a square prism (a cuboid).

Comments

  1. Very beautiful!  I've been editing the Wikipedia articles on honeycombs a bit.  It's great to see your pictures there.  I'd like to make the theory a bit more accessible to Wikipedia readers... though I haven't gotten very far, and I might not have time; I've just changed the start of the entries on the four hexagonal tiling honeycombs {6,3,3}, {6,3,4}, {6,3,5} and {6,3,6}.

    I have one tiny suggestion regarding these pictures.  They'd be more dramatic if there were more brightness contrast between the pale 'struts' and the colored 'background'.  On Visual Insight I've taken the liberty of increasing this contrast a bit using Irfanview.  But you could probably do a better job.

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  2. I'm very glad to hear about your wiki edits with a focus on accessibility John Baez!

    Thank you for the suggestion too. I like the image changes you made on Visual Insight. I am working on the truncated versions next, so I'll experiment with improving contrast while rendering those. If we find something we really like, I can regenerate the existing images.

    Please feel free to send more suggestions if you have them (I've not been super-happy with the initial scheme for background colors for instance, but have stuck with it in the absence of opinion.)

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