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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.
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LaoOne 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.
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What book discusses the platonic solids?
The book called Platonic Solids: The experience
How many edges does a platonic solids have?
There are different numbers on the different platonic solids.
Who descoverd the platonic solids?
We don't know for certain who discovered the platonic solids first. However, Pythagoras is credited by some sources as discovering the platonic solids first. Other sources credit Theaetetus as being the first to describe all five platonic solids and proving that these are the *only* platonic solids.
How did the platonic solids get their name?
The Platonic solids were name after the Greek philosopher Plato, who theorized that the classical elements were constructed from the regular solids.
Who proved that only five platonic solids exist?
Euclid was the one who proved that there are only five platonic solids.
