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Q: Must all the edges of a semiregular polyhedron be the same length?

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A polyhedron must have at least 4 faces, at least 4 vertices and at least 6 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 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.

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.

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.

Related questions

A polyhedron must have at least 4 faces, at least 4 vertices and at least 6 edges.

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.

A polyhedron is in a subclass of geometric solids. The difference is that a polyhedron must have flat faces and straight 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.

It must be a very strange shape. The numbers do not satisfy the Euler characteristic for any simply connected polyhedron.

A polyhedron, be definition, must be 3-dimensional. Therefore, there can be no such thing as a 2-d polyhedron

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.

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

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.

A polyhedron is a generic term for 3 dimensional objects which are bounded by polygonal faces. They can have 4 or more vertices, 6 or more edges and 4 or more faces. The numbers of vertices (V), edges (E) and faces (F) must also satisfy the Euler characteristic: F + V = E + 2.

In order for an object to qualify as a cube, it must satisfy these properties: * 6 faces (like a die), 12 edges, 8 corners * all it's edges must be equal length * all it's faces have equal area If the area of the cube is 294, then the sum of it's 6 faces' area is 294 So... The area of one face is 294 ÷ 6 = 49 If all it's edges have equal length, then each face is a square. The area of a square is length × length = length = length² = 49 So... the length of one edge is the square root of 49 = 7, -7 Since you are looking for a length, -7 is not an option. The length of the edge is 7

A pyramid cannot have 13 edges: it must have an even number of edges.

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