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Why does a Platonic solid look the same no matter which vertex you position at the top?
Wiki User
∙ 11y ago
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.
Wiki User
∙ 11y ago
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Why can a regular hexagon not be the face of a platonic solid?
Three regular hexagons meeting at a vertex would form a tessellation. So they would form a plane not a solid.
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.
Is a cone a Platonic solid?
No, a cone is not a Platonic solid. The Platonic solids are the five regular polyhedra: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
Why cant you use regular polygons as the faces of a platonic solid?
The faces of Platonic solids are regular polygons...
A cube is the only prism which is a Platonic solid?
No; platonic solids are tetrahedron, cube, octahedron, dodecahedron, icosahedron.
What platonic solid is a pyramid?
The platonic solids are: a tetrahedron, a cube, an octahedron, dodecahedron and icosahedron. A pyramid has a base with triangles attached to it with a common vertex. The platonic solid that is a pyramid is a tetrahedron (a triangular based pyramid).
What is the definition of a platonic solid?
From Wikipedia: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. Moreover, all its edges are congruent, as are its vertices and angles.
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 can a regular hexagon not be the face of a platonic solid?
Three regular hexagons meeting at a vertex would form a tessellation. So they would form a plane not a solid.
What is an octahendron?
Well a Regular Octahendron is simply a platonic solid composed of 8 equilateral triangles, four of which meet at each vertex.
Which figure has faces that are congruent to its bases?
A Platonic solid.A Platonic solid.A Platonic solid.A Platonic solid.
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.
Why dont the Platonic solid look alike?
Platonic solids are convex regular polyhedra. The faces of a platonic sold are all congruent polygons and they are all regular.The number of sides that meet at a vertex is the same for all vertices. When the sides are triangles, the platonic sold is a tetrahedron. This will NOT look the same as a cube where the sides are squares. So how the Platonic solid looks depends on the shape of its sides and very one of the five of them has different shaped sides.
Is a cylinder a platonic solid?
No. All the faces of a Platonic solid are identical regular polygons.
What is the difference between a platonic solid and a polyhedron?
WHat is the difference between polyheron and platonic solid
Is a trapezoid a platonic solid?
A trapezoid is not a platonic solid. There are only five platonic solids. They are the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron.
Is a cone a Platonic solid?
No, a cone is not a Platonic solid. The Platonic solids are the five regular polyhedra: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
