Platonic Solids Essay- This is an essay i wrote for math class on why there are exactly five regular polyhedra, and why there can never be any more of them.

Platonic Solids Essay I think that there ar exactly five strong polyhedra, and I intend to study why there be exactly five polyhedra. Ok, firstly, we adopt to identify what the five polyhedra atomic play 18. They atomic number 18 the tetrahedron, the pulley, the octahedron, the icosahedron, and the dodecahedron. All of these be fastness polyhedra kick in something in common. For on an individual basis shape, apiece of its faces are the comparable fastness polygon, and the same consider of faces meet at a top. This is the radiation pattern for forming regular polyhedra. today we need to collapse the shapes of the faces, and the number of them conflict at a extremum. The faces for the tetrahedron, octahedron, and the icosahedron are either triangles, and the number of faces skirmish at a pinnacle is 3, 4, and 5 respectively. The faces in a cube are all squares, and the number of faces meeting at a vertex is 3. Finally, for the dodecahedron, there are 3 pentagons meeting at each vertex. The aboriginal expression is that the interior angles of the polygons meeting at a vertex of a polyhedron add up to little than 360 degrees. This is the key element in making sure if the conditions for constructing a polyhedron lactate true.

Now we essential analyze the shapes and see which ones hatful cave in a regular polyhedron. For any shape, you cannot engross less than 3 faces meeting at a vertex because it is impossible to produce a closed 3-D build with less than 3 faces meeting at a vertex. So we can rule that taboo for each shape. For a triangle, since the angles are 60 degrees each, you can have 3, 4, and 5 faces meeting at a vertex without the angulate defect being 360 or more, and all of those are polyhedra I... If you loss to get a skilful essay, order it on our website: Orderessay

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