Talk:Prismatoid

pentagrammic crossed-antiprism
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)

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)

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&#39;Rourke (talk) 23:24, 16 September 2008 (UTC)

Volume
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) 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)