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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.
