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Two metrics on the same set are said to be topologically equivalent of they have the same open sets. So if an open subset, U contained in M is open with respect to one metric if and only if it is open with respect to the other metric. Another way to think of this is two objects are topologically equivalent if one object can be continuously deformed to the other. To be more precise, a homemorphism, f, between two topological spaces is a continuous bijective map with a continuos inverse. If such a map exists between two spaces, the are topologically equivalent.
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How is a hexagonal prism alike to a hexagonal pyramid?
Both have at least one hexagonal face (base). Both have six faces that are topologically equivalent (either rectangles, or triangles).
What is a regular decahedron?
None of the 32,300 topologically distinct decahedra is regular.
How many parallel faces does an octahedron have?
There are 257 topologically different convex octahedra. Many of these will have no parallel faces. It can have four pairs of parallel faces.
How many edges on a octahedron?
An octahedron is a closed 3-d shape with 8 polygonal faces. There are 257 topologically different convex octahedra. Octahedra can have 12 to 18 edges.
How many vertices are on a octahedron?
An octahedron is a closed 3-d shape with 8 polygonal faces. There are 257 topologically different convex octahedra. An octahedron can have 6 to 12 vertices.
