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 unbendable polyhedra, and I intend to stir why there be exactly five polyhedra. Ok, firstly, we emergency to identify what the five polyhedra argon. They are the tetrahedron, the cube, the octahedron, the icosahedron, and the dodecahedron. All of these are well-ordered polyhedra watch something in common. For separately shape, apiece of its faces are the equivalent regular polygon, and the same numerate of faces meet at a top. This is the radiation pattern for forming regular polyhedra. today we need to crumble the shapes of the faces, and the offspring of them merging at a extremum. The faces for the tetrahedron, octahedron, and the icosahedron are all triangles, and the number of faces skirmish at a vertex 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 ab original notice is that the interior angles of the polygons meeting at a vertex of a polyhedron add up to less than 360 degrees. This is the key element in making sure if the conditions for constructing a polyhedron lactate true.

Now we moldiness analyze the shapes and see which ones pile cave in a regular polyhedron. For any shape, you cannot use less than 3 faces meeting at a vertex because it is impossible to produce a closed 3-D figure with less than 3 faces meeting at a vertex. So we can rule that turn out for each shape. For a triangle, since the angles are 60 degrees each, you can have 3, 4, and 5 faces m eeting at a vertex without the angulate defe! ct being 360 or more, and all of those are polyhedra I... If you emergency to get a full essay, order it on our website: BestEssayCheap.com

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