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What polyhedron have some a face but no edges and no vertices?
A polyhedron must have at least 4 faces, at least 4 vertices and at least 6 edges.
Is it possible for convex polyhedron to have 6 faces 8 vertices and 10 edges?
No, F + V = E + 2That's Euler's polyhedron formula (or Theorem). For a normal 3-d polyhedron to exist it must conform to that equation.
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.
Is the shape of the football polygon?
No because a polygon is a plane figure. A football is a bit like a polyhedron, but all the faces of a polyhedron must be flat and, because of inflation, those of a football are not.
Cylinder faces edges vertices?
Euler's definition do not apply to curved solids. faces must be polygons; they cannot be circles. using the conventional definitions of faces, edges and vertices, This question causes frustration for teachers and students. Euler's definitions of edges, faces and vertices only apply to polyhedra. Faces must be polygons, meaning comprised of all straight sides, edges must be straight, and vertices must arise from the meeting of straight edges. As such, a cylinder has no faces, no edges and no vertices, using the definitions as they apply to polyhedra. You need to create a different set of definitions and understandings to apply to solids with curved surfaces.
What polyhedron have some a face but no edges and no vertices?
A polyhedron must have at least 4 faces, at least 4 vertices and at least 6 edges.
How many faces and edges does a 3d polyhedron have?
The only thing that can be said that there must be at least 4 faces and at least 6 edges and that the polyhedron must satisfy the Euler criterion which requires that: Faces + Vertices = Edges + 2.
What is the difference between a geometric solid than a polyhedron?
A polyhedron is in a subclass of geometric solids. The difference is that a polyhedron must have flat faces and straight edges.
How do you tell if a shape is polyhedron?
A shape is a polyhedron if it is a three-dimensional figure made up of flat polygonal faces, straight edges, and vertices. Each face must be a polygon, and the edges where the faces meet must be straight lines. Additionally, a polyhedron should enclose a volume, meaning it cannot have holes or gaps. If a shape meets these criteria, it can be classified as a polyhedron.
Is it possible for convex polyhedron to have 6 faces 8 vertices and 10 edges?
No, F + V = E + 2That's Euler's polyhedron formula (or Theorem). For a normal 3-d polyhedron to exist it must conform to that equation.
A has twice as many edges as faces.?
Well, isn't that just delightful! It sounds like A is a special kind of shape called a polyhedron. You see, in a polyhedron, each edge connects two faces together. So if A has twice as many edges as faces, it must be a very harmonious shape with a lovely balance between its edges and faces.
What has 9 faces 12 edges and 18 vertices?
It must be a very strange shape. The numbers do not satisfy the Euler characteristic for any simply connected polyhedron.
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.
How does a 2-d polyhedron look?
A polyhedron, be definition, must be 3-dimensional. Therefore, there can be no such thing as a 2-d polyhedron
What has 5 faces 6 edges and 4 vertices?
No regular polyhedron can have these qualities: F + V - E must equal 2. - a three-sided pyramid has 4 faces, 6 edges, and 4 vertices. - a four-sided pyramid has 5 faces, 8 edges, and 5 vertices
How do you know That it is a solid polyhedron?
A solid polyhedron is characterized by having flat polygonal faces, straight edges, and vertices. It is three-dimensional and completely enclosed, meaning it occupies a defined volume in space. Additionally, the arrangement of its faces must ensure that they meet at edges and vertices, forming a closed shape without any gaps or openings. Examples include cubes, tetrahedra, and octahedra.
How many faces and vertices does a gemstone have with 22 edges?
The number of vertices and faces is 2 more than the number of Edges according to Euler's formula. So a gemstone with 22 edges must have a total of 24 faces and vertices.
