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im doing a question that involves a shape with 8 faces, 10 vertices and 16 edges. Can anyone enlighten me as to what this shape is called? Many Thanks

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It's not clear to me that the shape is unique given only this information. –  Qiaochu Yuan Mar 15 '11 at 14:32
@Qiaochu: I believe it is unique. It takes a lot cases to prove this though. There are only a couple of possible degree sequences, and only a couple of possible choices for the sequences of faces, and eventually we eliminate all but the degree sequence 3,3,3,3,3,3,3,3,5,5 and the possibility that all the faces are squares. I wonder if there is a slicker way? –  Eric Naslund Mar 15 '11 at 14:51
I am going to leave my previous comment, but Dan Moores answer definitely shows it is completely wrong. –  Eric Naslund Mar 15 '11 at 16:47

3 Answers 3

Additionally, any polyhedron represented at this link could also be the shape you're looking for:


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This seems quite definitive. –  Grumpy Parsnip Mar 15 '11 at 16:17

The tetragonal trapezohedron seems to fit your bill.

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This paper, that enumerates and shows plane 3-connected graphs for the convex polyhedra with 4 to 8 faces, may be of interest: Federico, P. J. Polyhedra with 4 to 8 faces. Geometriae Dedicata 3 (1974/75), 469–481.

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