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 Post subject: What would this shape be called/look like?
PostPosted: Tue Mar 12, 2013 7:28 pm 
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If you take a rhombic dodecahedron and truncate both the edges and the corners, while leaving all the original faces intact as well, you end up with a polyhedron with exactly 50 faces. What's it called? And are there pictures of it?


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 Post subject: Re: What would this shape be called/look like?
PostPosted: Tue Mar 12, 2013 9:35 pm 
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Pentacontahedron:



http://www.georgehart.com/virtual-polyh ... hedra.html

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Last edited by KelvinS on Tue Mar 12, 2013 9:39 pm, edited 3 times in total.

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 Post subject: Re: What would this shape be called/look like?
PostPosted: Tue Mar 12, 2013 9:36 pm 
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I'm not sure if it has an official name. It seems to be referred to as the "Fully Truncated Rhombic Dodecahedron":

https://en.wikipedia.org/wiki/Truncated ... decahedron

Image

Edit: only one of the vertex types is truncated there. You'd also need to truncate the 4 vertices around each square face.

Edit 2: I see you said truncating edges which isn't discussed above or shown.

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 Post subject: Re: What would this shape be called/look like?
PostPosted: Tue Mar 12, 2013 9:50 pm 
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I was going to point you to this link:

http://www.shapeways.com/model/145512/50-side-dice-hollow.html

I believe it is the shape you describe and like KelvinS this seller calls it the pentacontahedron. But technically I believe pentacontahedron just means a 50 sided polyhedron, not necessarily this specific shape. On that front I may agree with Brandon. I'm not sure if it has an official name.

Carl

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 Post subject: Re: What would this shape be called/look like?
PostPosted: Tue Mar 12, 2013 10:36 pm 
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Thanks guys! :D


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 Post subject: Re: What would this shape be called/look like?
PostPosted: Wed Mar 13, 2013 1:24 am 
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Truncating both types of vertexs until the original edges vanish would produce the rectified rhombic dodecahedron, whish would have 12 rhombic faces, 6 square faces, and 8 triangular faces.
Truncateing the vertexes of the rectified rhombic dodecahedron would then produce the polyhedron you describe, turning the rhombi into irregular octagons, the squares into octagons, and triangles into hexagons and adding 24 quadralateral faces. I think the name for this kind of transformation is called cantellation, though I might be misspelling that or confusing it with a different transformation.

So, if I am not mistaken, the shape you describe would be a cantellad rhombic dodecahedron.

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 Post subject: Re: What would this shape be called/look like?
PostPosted: Fri Mar 29, 2013 9:49 am 
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I love this shape and made a skewb mod out of it.

Attachment:
cw_50-face zonish (1).jpg
cw_50-face zonish (1).jpg [ 1.44 MiB | Viewed 911 times ]

Attachment:
cw_50-face zonish (2).jpg
cw_50-face zonish (2).jpg [ 1.59 MiB | Viewed 911 times ]


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 Post subject: Re: What would this shape be called/look like?
PostPosted: Fri Mar 29, 2013 11:51 am 
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Nice!

How about a Master Skewb version where the cut lines coincide with as many edges as possible?


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