Talk:Prismatoid

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Polyhedra

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pentagrammic crossed-antiprism[edit]

Is the 4th object pictured, the pentagrammic crossed-antiprism, really a prismatoid? If so, why? It seems to have vertices in places other than the two parallel planes. mg 17:00, 30 November 2007 (UTC)[reply]

See Prismatic uniform polyhedron for more examples. There's just two planes of vertices, but the edges intersect so it may look like there's more vertices - just like the pentagram has 5 vertices but could be 10 if you thought there was vertices at the intersections. Tom Ruen 18:06, 30 November 2007 (UTC)[reply]

I altered the definition of prismoid to insist that the side faces are quadrilaterals. See, e.g., http://mathworld.wolfram.com/Prismoid.html. There is some ambiguity out there on this topic, but I believe simply requiring the same number of vertices is too weak a condition. Joseph O'Rourke (talk) 23:24, 16 September 2008 (UTC)[reply]

Volume[edit]

This was added anonymously to the intro, corrected by someone else, and there's no evidence where it comes from or its correctness. Tom Ruen (talk) 01:33, 17 January 2010 (UTC)[reply]

If the areas of the two parallel faces are A₁ and A₃, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A₂, and the height (the distance between the two parallel faces) is h, then the volume of the prismatoid is given by $V=h{\frac {(A_{1}+A_{3})}{6}}+h{\frac {2A_{2}}{3}}$ .

Tom Ruen

The formula follows by very elementary means. I have restored it with an explanation. JamesBWatson (talk) 14:50, 20 January 2010 (UTC)[reply]