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Find the symmetries of the Platonic Solids: Cube, Tetrahedron, Octahedron, Icosahedron, and Dodecahedron. I. You need to...

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Basic Math

Find the symmetries of the Platonic Solids: Cube, Tetrahedron,Octahedron, Icosahedron, and Dodecahedron.

I. You need to describe with words the planes of reflectionalsymmetry and identify how many there are in any of the categoriesfound.

II You need to describe with words the axes(lines) of rotationalsymmetry. For each type of axis, determine how many there are andthe order of rotation.

Answer & Explanation Solved by verified expert
3.9 Ratings (551 Votes)
A plane of symmetry divides a three dimensional shape into two congruent halves that are mirror images of each other This means that if you cut a 3 D object from any side or angle and it turns out to be congruent with the other its called a plane of symmetry a Dual polyhedra Every polyhedron has a dual or polar polyhedron with faces and vertices interchanged The dual of every Platonic solid is another Platonic solid so that we can arrange the five solids into dual pairs The tetrahedron is selfdual ie its dual is another tetrahedron The cube and the octahedron form a dual pair The dodecahedron and the icosahedron form a dual pair If a polyhedron has Schlfli symbol p q then its dual has the symbol q p Indeed every combinatorial property of one Platonic solid can be interpreted as another combinatorial property of the dual One can construct the dual polyhedron by taking the vertices of the dual to be the centers of the faces of    See Answer
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