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?

Pentacontahedron:



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

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



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.

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

Thanks guys!

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.

I love this shape and made a skewb mod out of it.

Nice!

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