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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.
Why is a cylinder and a Mobius strip NOT topologically equivalent?
A cylinder and a Möbius strip are not topologically equivalent because they have different properties regarding their boundaries and orientability. A cylinder has two distinct edges (boundaries) and is orientable, meaning it is possible to distinguish a "left" side from a "right" side. In contrast, a Möbius strip has only one edge and is non-orientable, meaning if you travel along its surface, you can end up on the "opposite" side without ever crossing an edge. These fundamental differences in structure prevent the two shapes from being transformed into one another through continuous deformation.
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.
What is leonhard euler's rule for corners edges and faces?
For a simply connected convex polyhedron , that is, shapes that are topologically equivalent to a sphere, F - E + V = 2 where F = faces, E = edges and V = vertices. For shapes that are topologically equivalent to a sphere with one hole in it (torus or doughnut shape), F - E + V = 0 For shapes that are topologically equivalent to a sphere with two holes in it F - E + V = -2 For shapes that are topologically equivalent to a sphere with three holes in it F - E + V = -4 and so on.
If you have twenty vertices and thirty edges how many faces do you have?
Without further information, there is no unique answer. If the surface is topologically equivalent to a sphere, then the answer is 12. (chi = 2) If the surface is topologically equivalent to a torus (donut), then the answer is 10. (chi = 0) Given the Euler number of the surface, chi, F = chi - V + E, where F is the number of faces, V is the number of vertices, E is the number of edges.
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.
What is the polyhedra with 7 faces?
It is a heptahedron. There are 34 topologically distinct convex heptahedra.
Why is a cylinder and a Mobius strip NOT topologically equivalent?
A cylinder and a Möbius strip are not topologically equivalent because they have different properties regarding their boundaries and orientability. A cylinder has two distinct edges (boundaries) and is orientable, meaning it is possible to distinguish a "left" side from a "right" side. In contrast, a Möbius strip has only one edge and is non-orientable, meaning if you travel along its surface, you can end up on the "opposite" side without ever crossing an edge. These fundamental differences in structure prevent the two shapes from being transformed into one another through continuous deformation.
8 faced 3D shape?
It is an octahedron. There are 257 topologically distinct octahedra: with 6 to 12 vertices.
How many shapes does a dodecahedron have?
There are around 6.4 million topologically different convex dodecahedra, plus concave ones.
What does equivalent to mean?
Equivalent to means equal to or the same as.
Does equivalent mean equal?
To be equivalent means to be the same as a value or thing. So yes, it does mean equal.
What are equivalent ratios to 110?
If you mean 1 to 10 then the equivalent ratio is 10 to 100If you mean: 1 to 10 then the equivalent ratio is 10 to 100
What does equivanlent mean?
If you mean "equivalent", it means equal to.
