are all polygons 3d objects?
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polygons are 2 dimensional shapes. they must have all straight sides and they must be closed. some examples are squares triangles, etc.  circles aren't because they  have 1 curved side.\n\npolyhedrons are 3-d shapes that have all flat sides and have no openings. ex: cube. spheres, cones, and cylinders are not because they all have curved sides.
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Mathematically n dimensions can be described but our experience is only 3 dimensions So the properties of fourth dimensonal shapes can be mathematically described and a fourth dimensional quantity that is in units^4 can also be calculated\n\nThis is an argument that the 4th dimension is time. That cannot be the case when one considers the properties in 3d are L, L, and L One would immediately envisage that the 4th, 5th .... nth dimensions would also all be L\n\nA tesseract, the 4 dimensional equivalent to the 2 dimensional square and 3 dimensional cube, is not a time related object at all. Its 3D projection can be build and the objects equivalent of a 2D shadow seen easily. In 4-space it occupies L^4 units^4. Wikepedia has some interesting information and projections of a tesseract
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Well, lets see if we can generate a pattern.\n\nA 3-sided polygon (aka a triangle) has no diagonals\nA 4-sided has 2\nA 5-sided has 5 (1-3, 2-4, 3-5, 4-1, 5-2)\nA 6-sided has 9 (1-3, 1-4, 1-5, 2-4, 2-5, 2-6, 3-5, 3-6, 4-6)...\nand so on.\n\nA polygon with n sides has n(n-3)/2 diagonals. The answer for 42 is left as an exercise for the reader ;)
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I don't think so. Does earth have an end? Nope, not in 2D. So universe may not have an end in 3D, but can be multidimensional
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Zeroth dimension = point\nFirst dimension = line\nSecond dimension = square\nThird dimension = cube\nFourth dimension = tesseract\nFifth dimension = decateron\n\nThe rests have names (I've lost the website), but what you are listing is the names of polygons (at least after the tesseract), all two-dimensional objects.\n\nA two dimensional object with:\n3 sides = triangle\n4 sides = square\n5 sides = pentagon\n6 sides = hexagon\n7 sides = heptagon\n8 sides = octagon\n9 sides = nonagon\n10 sides = decagon\n\nSee the below for the construction of the rest of the names:
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Triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon
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No. xy = k is an hyperbola in 2D. xy = kz is an hyperboloid on 3D.
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http://www.mathleague.com/help/geometry/polygons.htm
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Disagree.  You can have a square that has sides of 8 inches and another with sides of 3 inches.  They are similar because the angles are congruent, and the sides are in proportion, but they are NOT congruent figures.  (Same SIZE and shape).  If two polygons are congruent, then their sides are in a scale factor of 1:1 and their angles are congruent, thus they are similar also.
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word for word from MathWorld\n\nA regular polygon is an -sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular and equilateral). Only certain regular polygons are "constructible" using the classical Greek tools of the compass and straightedge. \n\nThe terms equilateral triangle and square refer to the regular 3- and 4-polygons, respectively. The words for polygons with  sides (e.g., pentagon, hexagon, heptagon, etc.) can refer to either regular or non-regular polygons, although the terms generally refer to regular polygons in the absence of specific wording.
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triskaidecagon\n\nor a 13-sided polygon, haha.\n\nCheck the source for polygon names from 1-20 sides  :)
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The edges are anywhere that 2 of the surfaces connect.  If you are given enough information, say the coordinates of one of the corners and some combination of length, width, height, surface area or volume, you should be able to draw it in 3-dimensional space.
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It hasn't always been hexagons.  The balls used to be made from curved four sided panels.  Using hexagons ensures that the ball is more spherical.
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One possible three-dimensional cross section of a cone in the fourth dimension is a sphere. (Think of the analogy of a cross section of a cone in 3 dimensions being a circle. It can also be an ellipse or hyperbola.) There are some interesting illustrations of such cross sections (not only spheres, but some other shapes analogous to the hyperbola or ellipse) at the following link:\n\nhttp://www.well.com/~abs/SIGGRAPH96/4Dtess.html
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a 20 faced polyhedron is called an \nicosahedron-the faces are equilateral\ntriangles\na 20 sided polygon is called an\nicosagon\n\ni hope that this helps
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Is this a real-world or mathematically-defined object?  Three dimensional?  Not enough info.\nIf a real object: You can do all sorts of hanging and balancing, but 3D objects, and especially those that are not clean geometric shapes (picture a randomly shaped rock) can be tough, requiring the assignment of a coordinate system, attachment of balancing pivot points, etc.  2D real objects are a snap: Hang from any point, draw a vertical line through the point, repeat at another point; where the lines intersect is the CM.  Here's a neat trick I read somewhere for finding the CM of something long & skinny like a stick:  Hold it horizontal, resting on two small sticks that are far enough apart so the CM is in between.  Slowly move the sticks together; they will meet at the CM!  I think you can do this with a flat 2D piece and three pins if you happen to have three hands.
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Go to yahoo.com\n\nIn the search engine,  type in; \n\ndiagonal polygons +images\n\nYou will actually get images of diagonal polygons at that point!