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In a platonic solid all faces are identical regular polygons. A polyhedron has faces, edges, and vertices. The numbers of each are related by Euler's formula, V+F=E+2
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Other than squares the polygons that can be the face of a Platonic solid are and?
equilateral triangles and regular pentagons
What is a solid with a polygon for each face?
A solid with a regular polygon for each face is known as a perfect solid.
What is a flat surface of a geometric solid?
A face
What is a solid figure with 10 faces called?
A decaredra is the ten face solid figure.
Best describes the surface area of a solid figure?
The sum of the areas of each face of the solid.
What polygon can be a face of a Platonic solid?
A triangle, square or pentagon.
What polygons can be the face of a platonic solid?
A triangle, square or pentagon.
Other than squares the polygon that can be the face of a platonic solid are and?
triangles and pentagons
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
Other than squares the polygons that can be the face of a Platonic solid are and?
equilateral triangles and regular pentagons
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.
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 makes a solid a regular platonic solid?
A Platonic solid is a solid all of whose face are regular and congruent polygons.There are five of these:A Tetrahedron. Four faces, each an equilateral triangle.Ad InfoA Hexahedron (Cube). Six faces, each a square.An Octahedron. Eight faces, each an equilateral triangle.A Dodecahedron. Twelve faces, each a regular pentagon.An Icosahedron. Twenty faces, each an equilateral triangle.
What platonic solids do not have a triangular face?
A cube and a dodecahedron.
What is solid face in geometry?
A contradiction. A solid is a 3-dimensional object, a face is 2-dimensional. Hence you cannot have a solid face.
What is a solid with a polygon for each face?
A solid with a regular polygon for each face is known as a perfect solid.
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.
