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A dual is almost like the opposite of a given polytope. For example, a regular octahedron is the dual of a cube.
Look at the similarities between duals with the example of a cube and regular octahedron:
Cube:
Vertices: 8
Edges: 12
Faces: 6
Edges per vertex: 3
Type of face: square (4-sided)
Regular Octahedron:
Vertices: 6
Edges: 12
Faces: 8
Edges per vertex: 4
Type of face: triangle (3-sided)
Both of these shapes can be put together to form a compound and can be rectified to form the same new shape: a cuboctahedron.
Also, duals can fit perfectly inside another where each edge touches the face of the other.
In this same way a regular dodecahedron is the dual of a regular icosahedron. Some polyhedra like the regular tetrahedron is the dual of itself. All polyhedra have duals. Polygons, polychora, and other polytopes can also have duals in a similar fashion.
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What is a self dual polyhedron?
For every polyhedron, there is a dual which is a polyhedron that has:a face where the first had a vertex,a vertex where the first had a face,the same number of edges.A self-dual polyhedron is a polyhedron whose dual is the same shape.All pyramids, for example, are self-dual.
What is the difference between the primal and dual?
The difference between primal and dual are that primal means an essential, or fundamental of an aspect where as dual means consisting of two parts or elements. Primal is one, dual is two.
How are platonic solids related?
One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.A tetrahedron is its own dual.A hexahedron (cube) and octahedron from a dual pair.A dodecahedron (cube) and icosahedron from a dual pair.One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.A tetrahedron is its own dual.A hexahedron (cube) and octahedron from a dual pair.A dodecahedron (cube) and icosahedron from a dual pair.One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.A tetrahedron is its own dual.A hexahedron (cube) and octahedron from a dual pair.A dodecahedron (cube) and icosahedron from a dual pair.One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.A tetrahedron is its own dual.A hexahedron (cube) and octahedron from a dual pair.A dodecahedron (cube) and icosahedron from a dual pair.
What is a dual-scale thermometer?
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Example of linear functional in dual space?
dual space W* of W can naturally identified with linear functionals
What is a sentence with dual in it?
She had a dual nature because of the disease. This is a sentence containing the word dual.
A sentence with the word dual in it?
This trailer has a dual axle.The man used a dual blade for shaving.There is a dual function on this keyboard (synthesizer).This machine and do dual tasks at the same time.
What is a sentence using the word dual?
This trailer has a dual axle.The man used a dual blade for shaving.There is a dual function on this keyboard (synthesizer).This machine and do dual tasks at the same time.
Is micromax x550 dual standby?
Yes. It is a dual sim phone with Dual standby.
What are the dual pairs for each of the platonic solids?
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.
A sentence for the word dual?
There was a dual between the 2 fighters. The one in red won the match.
What is a dual theme?
when something was dual themes
What is self dual logic function?
A self-dual logic function is a function that is identical to its dual
What is dual court systems?
What is dual court system
What is the dual process?
Dual channel process can use
Is lg gx200 dual active?
no its not a dual active...
What is the homonym for dual?
The homonym for "dual" is "duel".
