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A tetrahedron is its own dual.
An octahedron is the dual of a cube and conversely.
An icosahedron is the dual of a dodecahedron and conversely.
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What does each platonic solid represent?
Platonic solids are 3D shapes formed using only regular shapes. Only 1 type of regular shape is used to make a platonic solid. Platonic solids are the simplest and purest form of 3D shapes.
Meaning of each platonic solid?
There are 5 platonic solids which are the only 5 regular polyhedra (possible).Plato attributed 4 of them to the 4 elements:Fire ≡ TetrahedronEarth ≡ CubeAir ≡ OctahedronWater ≡ IcosahedronAristotle added the fifth element "Ether" saying the heavens were made of it; he did not associate the fifth platonic solid, the Dodecahedron, to it.
What is the Platonic Solid and How many are there and What are their names?
Answering your questions one at a time.1 - What is a platonic solid?A platonic solid is one with all faces congruent polygons, meaning that they all have the same number of sides, vertices and angle size.2 - How many are there?There are only and exactly five.3 - What are their names?TetrahedronCube (but when talking about Platonic solids, it is commonly referred to as a "hexahedron").OctahedronDodecahedronIcosahedronNote: These individual platonic solids can be identified by their unique Schlafli Symbol. This is demonstrated through the following:{p,q}p = Number of vertices at each faceq = Number of faces at each vertexSo for a dodecahedron, the Shlafli Symbol would be {5,3}, because a pentagon has five {5, or p} vertices, and at any individual vertex three {3, or q} faces meet.Understand? Great!
What is the name of the Platonic solid for which each face has a one-fourth probability of turning up when it is rolled?
tetrahedron
What are the properties of a platonic solid?
A Platonic solid is a regular, convex polyhedron. The same amount of edges must meet at each vertex, all the faces need to be uniform, and all the dihedral angles must be the same.
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.
What does each platonic solid represent?
Platonic solids are 3D shapes formed using only regular shapes. Only 1 type of regular shape is used to make a platonic solid. Platonic solids are the simplest and purest form of 3D shapes.
Each face is what polygon on a octahedron?
A regular octahedron is one of the platonic solids. Each of its faces is an equilateral triangle.
Instructions on how to make platonic solid?
There are only five geometric solids that can be made using a regular polygon and having the same number of these polygons meet at each corner. The five Platonic solids (or regular polyhedra) are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron
What are platonic solids and what do they look like?
The five Platonic solids are regular polyhedra. They are convex shapes which are created from regular polygonal faces, such that the number of faces meeting at each face is the same.The five are:tetrahedron - 4 triangular faces;hexahedron (or cube - 6 square faces;octahedron - 8 triangular faces,dodecahedron - 12 pentagonal facesicosahedron - 20 triangular faces.To see their images, search Google for Platonic Solids.
Which 2 solids have the same number of edges?
A rectangular prism (cuboid) and a hexagon-based pyramid, for example, both have 12 edges. Of the five Platonic solids, an octahedron and a cube each have 12 edges.
Meaning of each platonic solid?
There are 5 platonic solids which are the only 5 regular polyhedra (possible).Plato attributed 4 of them to the 4 elements:Fire ≡ TetrahedronEarth ≡ CubeAir ≡ OctahedronWater ≡ IcosahedronAristotle added the fifth element "Ether" saying the heavens were made of it; he did not associate the fifth platonic solid, the Dodecahedron, to it.
What are examples of platonic solids?
A Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex. They have the unique property that the faces, edges and angles of each solid are all congruent. Some examples are bricks, a dice, tissue boxes and houses.
What solids have 12 edges?
A cube has 12 edges as does an octahedron and those are the two platonic solids (convex polyhedra with congruent regular polygons as faces where the same number of faces meet at each vertice) with 12 edges.
Why is there only five platonic solids?
Similar to the two-dimensional case of the Chladni plate, the Platonic Solids are simply representations of waveforms in three dimensions. Each tip or vertex of the Platonic Solids touches the surface of a sphere in an area where the vibrations have canceled out to form a node. Thus, what we are seeing is a three-dimensional geometric image of vibration / pulsation within a sphere.In three dimensional spaces, there are ONLY FIVE natural frequency modes for spherical EM standing wave, resulting in the formation of the five Platonic solids shown below. Each platonic would be perceived as the formation of a stable form of matter, anything in between will tend to be unstable, and will degrade to its nearest stable form, giving off its extra elements as EM energy, with radioactive elements being such an example."Each shape can be attached to a multiple number of the same shape or other platonic shape to generate a bigger platonic solid or even a non platonic one, as happens during generation of crystals. In a way, one may regard a crystal lattice structure as a picture of the mechanism within the atom itself. So as you see, this theory works well at quantum level as well as at molecular level, which makes it unique."
What are the classical elements that are associated with each Platonic solid?
In Plato's theory (hence the 'Platonic' solids)Earth is associated with the cube, as it was strong and sank to the ground.Water is associated with the icosahedron, as it could move easily.Air is associated with the octahedron, as it could both penetrate and be mobile.Fire is associated with the tetrahedron, as it penetrated but did not flow.
What is the Platonic Solid and How many are there and What are their names?
Answering your questions one at a time.1 - What is a platonic solid?A platonic solid is one with all faces congruent polygons, meaning that they all have the same number of sides, vertices and angle size.2 - How many are there?There are only and exactly five.3 - What are their names?TetrahedronCube (but when talking about Platonic solids, it is commonly referred to as a "hexahedron").OctahedronDodecahedronIcosahedronNote: These individual platonic solids can be identified by their unique Schlafli Symbol. This is demonstrated through the following:{p,q}p = Number of vertices at each faceq = Number of faces at each vertexSo for a dodecahedron, the Shlafli Symbol would be {5,3}, because a pentagon has five {5, or p} vertices, and at any individual vertex three {3, or q} faces meet.Understand? Great!
