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trust nail down the bottom one, and keep all the strings taut. If you displace the top in any direction not parallel to a side, while keeping the strings taut, you have an oblique rectangular prism. Or, if you have trouble seeing that, move the top so that two edges stay in the same vertical plane they previously occupied, then (try to) move it perpendicular to that plane (it won't move a finite distance perpendicularly). In either case, the only right angles are on the top and bottom, and you have what must be called an oblique rectangular prism. The rectangular prisms must be the oblique rectangular prisms and the right rectangular prisms.
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The entry under faces in the table, too, was confusing because something like "p + 2" was expected, corresponding to the 2p and 3p in the vertices and edges entries, but that may just have been the result of the confusion set up by the initial paragraph, so I left it alone. An alternative --- p + 2
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current article (quote):"Take a polygon with n vertices, n edges. Its prism has 2n vertices, 3n edges, and 2 + n faces. Take a polyhedron with v vertices, e edges, and f faces. Its prism has 2v vertices, 2e + v edges, 2f + e faces, and 2 + f cells. Take a polychoron with v vertices, e edges, f faces
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If you slice a cylinder lengthways along its axis you get two shapes that have many of the properties of a prism, but are not prisms by the current definition. The solid has one flat face and one that is curved. It's volume is the area of the end face times it's length and its surface area can be
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I suggest "Take a polygon, polyhedron, or polychoron and sum the number of vertices w/ number edges, and number of faces,and,..,number of polychorons(=1). If one takes the prism of the original object, the corresponding sum is 3 times larger." I don't have a citation for this theorem, but it's easy
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To imagine an oblique rectangular prism, picture two identical rigid rectangles, with eyes at the vertices; tie the eyes together in pairs with 4 equal-length inelastic strings. Hold one horizontal; the other will hang below it, also horizontal; that's your right rectangular prism. Have someone you
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A std. dictionary, in case of the analogous right circular cylinder, does not waste the name "circular cylinder" on it: if you make the proper parallel oblique cuts off the ends of a right elliptical cylinder, you get an oblique circular cylinder; the oblique and right circular cylinders together
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I should have said that this along with the formulas, not formulae, already there would provide nice setting for the Pascal's triangle method of counting vertices edges etc on an n-cube:Just go to the nth row of triangle for 1+2x.(I know this method used to be on
Knowledge but I can't find it
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There is no inconsistency. Whoever wrote that paragraph was synthesizing from the comments of two older works, both of which mention that they hold minority opinions. I would not consider those older works to be reliable sources, but I'll rewrite that paragraph to mention the opposing
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found in the same way as a prism. But its not a prism and its not a cylinder. What is to stop this being considered a prism? (Aside from the obvious fact that the current definition exludes it by requiring polygonal faces).
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Moreover, the inclusion in this article of an image of these buildings is misleading and confusing given that only two of them are prisms, and one is not. One of my students was in fact confused by this image.
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sides (faces)?" I took the original intent of "an n-sided prism" to be an attempt to explain the nomenclature so, after clarifying the initial definition, I added the sentence about naming at the end.
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uses "side" to refer to (lateral) faces, while "n-sided polygon" uses "side" to refer to edges. The sense of "side" as "face" got the readers to ask "shouldn't a prism with an n-sided base have
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If i'm wrong, come up with a reliable reference that verifies the other supposed meaning. (If you do, the old article still needs work to clarify the illogical terminology.)
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Perhaps a prism could be "A solid with two congruent parallel faces, and where any cross section parallel to those faces is congruent to them." Thoughts?
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In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides.
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This passage, which i have rewrit, must reflect a failure of visual imagination by someone reconstructing what they had learned:
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I hope the usual maintainer of this page can fix these issues. I am not proficient in using wikipedia hypertags. Thanks!
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Where is the inconsistency in Euclid's definition of a prism? How is a triangular-based prism in conflict with it?
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and c cells. Its prism has 2v vertices, 2e + v edges, 2f + e faces, and 2c + f cells, and 2 + c hypercells."
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to prove from the above formulae, and there aren't citations for those formulae either.-Rich
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People reading that had found it confusing, largely because of the ambiguous use of "side":
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are among the types of right prism, with a rectangular and square base, respectively.
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It is unmathematical to waste those prism terms on the cuboid and the square cuboid.
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What consists of the base on a prism? Length times width?--
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