what angles are common to 5 faces of the pentagonal pyramid of which 12 make a regular dodecahedron?
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69.0948, 69.0948, 41.8104\n\nMore precisely, one of the base angles is equal to\n\narccos( 0.5 * sin(36) * ( 4 - sec(18)^2 )^0.5 / ( 1 + sin(36)^2 + sin(36) * sec(18) )^0.5 )
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b)hexagon(2d) or cube(3d).\nc)hemisphere\nd)triangle?\ne)net\nf)cube\ng)sphere\nh)decahedron\ni)dodecahedron\nj)parallelogram i think, if wat u mean is opposite equal  angles.
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A two dimensional figure is called a dodecagon and a 3D figure with 12 sides is called a dodecahedron.
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pentagon-5\nhexagon-6\npolygon-many
135770
trianglular pyramid has 8 edges and 5 verticles
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I'm a bit rusty on this but I believe what you have is  the group of transformations on a pentagon. x is a reflection across an axis of symmetry, y is a rotation where a vertex moves to the next adjacent vertex.\n\nI think that each G/<x> is going to be a refection across a different access of symmetry so it's a group, and each G/<y> is going to be another cyclic group of order 5 generated by a rotation of 1,2,3,4 sides.\n\nHope this helps its been decades since I did heavy group theory.
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Pentagon = 5, decagon = 10, quadrilateral = 4, and heptagon = 7.
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Make a Dodecahedron. That's what I did.
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If a pyramid is of 'n' number of sides then its base area 'A' is given by\nA = n*a^2*{cot(pi/n)}/4 where the base is a regular polygon of each side 'a'.\nIf the height is 'h' and the pyramid be right (i.e. the axis of symmetry is perpendicular to the base) then the volume of the pyramid 'V' is given by V = h*A/3.\nTherefore we can write h = 3*V/A.\nSo h = 3*V/[n*a^2*{cot(pi/n)}/4]\nor h = 12*V/[n*a^2*{cot(pi/n)}]\nThis is a relation from which height can be calculated if the volume no. of sides and length of each side of the pyramid be known.\n\nHowever, if the slant height 'L' is known then the height can be expressed as\nh = sqrt[L^2 - {0.5*a*cot(pi/n)}^2]\n\nBut, if the length of the slant surface edge 'E' is mentioned then the height is to be calculated from\nh = sqrt[E^2 - {0.5*a*cosec(pi/n)}^2]\n\nHope this helps.
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It is a triangular prism. It has 5 faces, 9 edges, and last but not least 6 vertices. There is your answer you have been waiting for this whole time!
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The five named after Plato are\n\nTetrahedron: 4 triangular faces, 4 vertices, 6 edges\nCube: 6 square faces, 8 vertices, 12 edges\nOctahedron: 8 triangular faces, 6 vertices, 12 edges\nDodecahedron: 12 pentagonal faces, 20 vertices, 30 edges\nIcosahedron: 20 triangular faces, 12 vertices, 30 edges\n\nEuler's Rule E + 2 = F + V applies to all five aolids.
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There is no rigorous definition of "corner" in geometry, so I assume you mean vertex, as pretending to have an answer by massaging the definitions is not appealing to me. Under peer review, a square pyramid has 5 vertices, period. It would be laughable to suggest otherwise.\nIf your figure is a convex polyhedron, then no such polyhedron exists, as the Euler sum 4 - 8 + 5 = 1 when it should be 2 for such a polyhedron.\nSince you did not specify the type of "figure" you are looking for, I can visualize many less rigorous shapes than convex polyhedra with the properties you need.
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Good question, but I think you meant pentagon.\n\nIf you had a regular pentagon with a side of 1, then the triangle formed any two adjacent sides of the pentagon, the third side equals Phi.\n\nTo check we can use the law of Sines.\n\nSin A / a = Sin B / b = Sin C / c\n\nEach interior angle of a regular polygon is found by this formula:\n\n180(n - 2) / n, when n = the number of sides the polygon has.\n\nSo, for a regular pentagon\n\n180(5 - 2) / 5\n180(3) / 5\n540 / 5\n108 degrees\n\nSince the triangle we formed is an isoscles one, the other 2 angles can be found out by subtracting 108 from 180 and dividing the result by 2.\n(180 - 108)/2 = 72/2 = 36 degrees\n\nSin 108 / Phi = Sin 36 / 1\n\nThe formula for Phi is:\n5 ^ .5 * .5 + .5\n\nArcSin(Sin 108 / (5 ^ .5 * .5 + .5)) = \n= ArcSin(0.9510565163 / 1.618033989) = \n= ArcSin(0.5877852523) = 36
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octahedron - eight sides\n\nif it is regular, all sides are the same\n\n32 / 8 is 4, there are 4 sq. in per side
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HEPTAGON - a seven-sided polygon.\n\nTRIANGULAR PYRAMID - a pyramid with a triangular base and 3 triangular faces.\n\nSCALENE TRIANGLE - a triangle none of whose sides have equal length. The angles don't have the same measures, too.\n\nISOSCELES TRIANGLE - a triangle 2 of whose sides have equal measures. Therefore, the angles opposite the congruent sides have equal measures also.\n\nEQUILATERAL TRIANGLE - a triangle all of whose sides have equal measures. The angles have equal measures, too.\n\nRIGHT TRIANGLE - a triangle 1 of whose angles has a measure of 90 degrees. The other 2 angles have measures that are less than 90 degrees. The side opposite the 90-degree angle is the longest side and is called the hypotenuse. The other sides are called legs.\n\nSPHERE - is shaped like a ball (round).\n\nCONE - it is a pyramid with a circular base.\n\nDECAGON - a polygon with 10 sides.\n\nDODECAGON - a polygon with 12 sides.
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You should be able to picture it. Or at least, find a D+D player and look at a 12-sided die.\n\nOne half of this is a pentagon, surrounded on each of the 5 edges by other equal-sized pentagons.  The pentagon has 5 edges, and from each of the five corners is another edge which reaches to the 'equator' of the thing.  The bottom half is identical, with anoth 10 edges just like the flipside. Finally, around the 'equator', is another 5 edges.\n\n25 edges.  Don't need formulas, just good 3-D visualization skills.\n\nPS  It's 'polyhedron', by the way.  Polyhedra is plural.  Saying 'a polyhedra' is just like saying 'a women'.
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A pentagon has 5 sides of equal length if that is what you are asking.