document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207316>Question 1207316</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you let me know the number of planes of symmetry and the number of axes of rotation for the following?\r<BR>\n" );
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document.write( "(i) Cylinder<BR>\n" );
document.write( "(ii) Cone<BR>\n" );
document.write( "(iii) Square based pyramid<BR>\n" );
document.write( "(iv) Rectangle based pyramid<BR>\n" );
document.write( "(v) Equilateral triangle based pyramid<BR>\n" );
document.write( "(vi) Isosceles triangle based pyramid<BR>\n" );
document.write( "(vii) Scalene triangle based pyramid </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845119 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52777)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Could you let me know the number of planes of symmetry and the number of axes of rotation for the following?<BR>\n" );
document.write( "(i) Cylinder<BR>\n" );
document.write( "(ii) Cone<BR>\n" );
document.write( "(iii) Square based pyramid<BR>\n" );
document.write( "(iv) Rectangle based pyramid<BR>\n" );
document.write( "(v) Equilateral triangle based pyramid<BR>\n" );
document.write( "(vi) Isosceles triangle based pyramid<BR>\n" );
document.write( "(vii) Scalene triangle based pyramid<BR>\n" );
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document.write( "(i)  For a cylinder, there are infinitely many of planes of symmetry.\r\n" );
document.write( "     They constitute a continuous set of planes.\r\n" );
document.write( "     They all are through the axis of rotation.\r\n" );
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document.write( "     There is one axis of rotation.\r\n" );
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document.write( "(ii)  For a cone, there are infinitely many of planes of symmetry.\r\n" );
document.write( "      They constitute a continuous set of planes.\r\n" );
document.write( "      They all are through the axis of rotation.\r\n" );
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document.write( "      There is one axis of rotation.\r\n" );
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document.write( "(iii) For a square based pyramid, there are 4 (four) planes of symmetry.\r\n" );
document.write( "      They all are through the altitude to the base.\r\n" );
document.write( "      Two of the four planes of symmetry are through diagonals of the square at the base.\r\n" );
document.write( "      Two other of the four planes of symmetry are through midpoints \r\n" );
document.write( "      of the opposite sides of the square at the base.\r\n" );
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document.write( "      There is one axis of rotation, but the rotations do not constitute a continuous set\r\n" );
document.write( "      of rotations. There are 4 (four) discrete rotations around the rotation axis \r\n" );
document.write( "      by the angles 90°, 180°, 270° and 360°.\r\n" );
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document.write( "(iv)  For a rectangle based pyramid, the rectangle at the base is assumed not to be a square.\r\n" );
document.write( "      There are 2 (two) planes of symmetry.\r\n" );
document.write( "      They all are through the altitude to the base.\r\n" );
document.write( "      These two planes of symmetry are through midpoints of the opposite sides \r\n" );
document.write( "      of the rectangle at the base.\r\n" );
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document.write( "      There is one axis of rotation, but the rotations do not constitute a continuous set\r\n" );
document.write( "      of rotations. There are only 2 (two) discrete rotations around the rotation axis \r\n" );
document.write( "      by the angles 180° and 360°.\r\n" );
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document.write( "(v)   For an equilateral triangle based pyramid, there are 3 (three) planes of symmetry.\r\n" );
document.write( "      They all are through the altitude to the base.\r\n" );
document.write( "      Each of these three planes of symmetry are through one vertex at the base and the midpoint \r\n" );
document.write( "      of the opposite side of the equilateral triangle  at the base.\r\n" );
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document.write( "      There is one axis of rotation, but the rotations do not constitute a continuous set\r\n" );
document.write( "      of rotations. There are only 3 (three) discrete rotations around the rotation axis \r\n" );
document.write( "      by the angles 120°, 240° and 360°.\r\n" );
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document.write( "(vi)  For an isosceles triangle based pyramid, the isosceles triangle at the base is assumed \r\n" );
document.write( "      not to be equilateral.\r\n" );
document.write( "      There is  1 (one) planes of symmetry.\r\n" );
document.write( "      It is through the altitude to the base.\r\n" );
document.write( "      This unique plane of symmetry is through the vertex of the triangle at the base \r\n" );
document.write( "      and the midpoint of the opposite side of the isosceles triangle  at the base.\r\n" );
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document.write( "      There is no axis of rotation.\r\n" );
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document.write( "(vii) For a scalene triangle based pyramid, the scalene triangle at the base is assumed \r\n" );
document.write( "      not to be isosceles.\r\n" );
document.write( "      There are no planes of symmetry.\r\n" );
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document.write( "      There is no axis of rotation.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.  All questions are answered.\r<BR>\n" );
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document.write( "In the future, please do not pack so many questions per post.\r<BR>\n" );
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document.write( "All the questions in the post are simple - any normal child of the age 7 - 9 years can understand their meaning,<BR>\n" );
document.write( "and (I am sure) every normal child can intuitively understand every relevant answer based on his common sense,<BR>\n" );
document.write( "even without any special training. Again, regular common sense is just enough.\r<BR>\n" );
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document.write( "The only thing to care about is using terminology accurately and constructing each answer in logical order.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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