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It is an arbitrary concept defined by Plato. actually the original 5 were different than the modern five, which were used by art instructors as Perspective props- they are: Sphere, Cube, Cone, Cylinder, and Pyramid! note the last one. somewhat oddly the ancient Egyptians did not draw in perspective- though they could not avoid the three dimensional look with statues, etc. That"s another story.
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What do the platonic solids look like?
The Platonic solids in modern Euclidean geometry are five regular polyhedra. These are three-dimensional objects that are bounded by regular polygonal faces. They are: Tetrahedron (or triangular pyramid): 4 triangular faces; Hexahedron (cube): 6 square faces; Octahedron: 8 triangular faces; Dodecahedron: 12 pentagonal faces; Icosahedron: 20 triangular faces. See link for more.
Why can t there be more then 5 platonic solids?
First, consider that at each vertex (point) at least three faces must come together, for if only two came together they would collapse against one another and we would not get a solid. Second, observe that the sum of the interior angles of the faces meeting at each vertex must be less than 360°, for otherwise they would not all fit together.
What is a platonic solid and how many are there and what are their names?
A Platonic solid is the 3-D shape equivalent of a polygon: it is a three dimensional figure whose sides are congruent, regular polygons, with identical vertices. Unlike the 2-dimensional case (in which there are infinitely many polygons) there are only 5 Platonic solids: * The tetrahedron, which has 4 triangular sides. * The cube (or hexahedron), which has 6 square sides. * The octahedron, which has 8 triangular sides. * The dodecahedron, which has 12 pentagonal sides. * The icosahedron, which has 20 triangular sides. Here is how the 5 Platonic solids were found, and how we know there aren't any more: Think about the sum of the angles at a vertex (by the definition of a Platonic solid, all vertices are identical). In the plane, angles around a vertex add up to 360 degrees, but we don't want the vertex to lie flat - otherwise, we'd end up with a huge flat sheet instead of a polyhedron. We also want at least 3 polygons around a vertex, because otherwise the result will become a flat figure without volume. If the sides are triangles, we can have 3 triangles around a vertex (getting the tetrahedron), 4 triangles around a vertex (getting the octahedron), or 5 triangles around a vertex (getting the icosahedron). We can't have 6 or more, because then the sum of angles wouldn't be less than 360. If the sides are squares, we can have 3 squares around a vertex, getting the cube. 4 squares around a vertex would mean the sum of angles is 360, and 5 or more is even more impossible. Finally, we can take 3 pentagons around a vertex, getting the dodecahedron; more pentagons will give us an angle sum of over 360. We can't use any shapes with more than 6 sides, because their angles are larger and we can't even fit 3 around a vertex. Even 3 hexagons will give an angle sum of 360 degrees, and anything more than that is even worse.
Five hundred is how much more than three hundred ninety-five?
500 - 395 = 105
How do you write 5.50 in word form?
You could say "five and a half" or more formally "five and five tenths"
Why are there a limited number of platonic solids?
Why are there a limited number of platonic solids?Read more: Why_are_there_a_limited_number_of_platonic_solids
Are platonic solids algebra?
Platonic solids, being three-dimensional objects with certain characteristics, would come under the category of geometry, not algebra. For more information on Platonic solids, see the Wikipedia entry or the Wolfram MathWorld description.
More about plantonic solids?
do you mean "Platonic" a Platonic solid is a convex regular polyhedron. more at http://en.wikipedia.org/wiki/Platonic_solid
What do the platonic solids look like?
The Platonic solids in modern Euclidean geometry are five regular polyhedra. These are three-dimensional objects that are bounded by regular polygonal faces. They are: Tetrahedron (or triangular pyramid): 4 triangular faces; Hexahedron (cube): 6 square faces; Octahedron: 8 triangular faces; Dodecahedron: 12 pentagonal faces; Icosahedron: 20 triangular faces. See link for more.
Are all pyramids platonic solids?
no
Why does a Platonic solid look the same no matter which vertex you position at the top?
The quick answer: because of the high degree of symmetry inherent in the Platonic solids. They are vertex-uniform, edge-uniform and face-uniform. If you hold several models of the same shape up by any vertex, all the models will appear the same. The same goes for holding the models up by any edge, or by any face. Read the following for a little more detail. Many solids that are not Platonic have symmetry as well, but the Platonic solids have some special symmetrical properties. You can create what are called 'dual polyhedrons' for solids, but the duals for Platonic solids are unique. You can form a Platonic solid's dual polyhedron by making the midpoint of every face of the original Platonic solid a vertex of the dual solid within the original. If you start with a cube, a hexahedron really, and make a new solid within it having vertexes at the centers of the square faces of the cube, the solid within will be an octahedron. Tetrahedrons are self-dual, squares and octahedrons are dual with one another, and dodecahedrons and icosahedrons are dual with one another. The dual polyhedron of a Platonic solid is always another Platonic solid. This is difficult to visualize without aid. See link for some clarification. On the dual relationship of a cube [6 faces, 8 vertexes] and octahedron [8 faces, 6 vertexes] breaking down the numbers of faces and vertexes might help. Each of the 6 faces of a cube contains one of the vertexes of the octahedron, and each of the vertexes of a cube will be at the center of one of the faces of the octahedron.
Are all solids metal?
some aren't Mercury is one metal that is liquid at room temperature.
What is the Difference between Regular and Irregular solids?
Regular object have equla sides and irregular dont
A number between 0 and 9 it cant be divided by 0 and is more then five what is it?
7
Why can't you squash a solid or a liquid?
In solids and liquids the molecules are already very close together so they can't be squeezed together much more than that. In a gas molecules are very spread out so they can be compressed.
How many faces does a polyhydra triangle have?
There are several triangular polyhedra. The simplest is a tetrahedron with 4 faces, but you can have a triangular dipyramid (two tetrahedra stuck together along one face) which has 6 faces. Then there is the icosahedron with 20 faces. The tetrahedron and icosahedron are Platonic solids, but there are many more.
Why can't we form a platonic solid using hexagons?
Because the hexagons angles are 120 degrees and the platonic solid wuld add up more than 360 degrees
