Q: Which shape has the same number of faces and corners?

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A pyramid has the same number of faces as vertices. A triangular pyramid has 4. A rectangular pyramid has 5. Check into Euler's Theorems.

cube

One possible pair is a cube and a parallelepiped. Vertices and corners are the same thing!

It is a cuboid or a cube

No faces, 1 edge, no corners. A circular disk has 1 face, but that is not the same as a circle.

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It is that of a cube.

A cube

A pyramid has the same number of faces as vertices. A triangular pyramid has 4. A rectangular pyramid has 5. Check into Euler's Theorems.

cube

One possible pair is a cube and a parallelepiped. Vertices and corners are the same thing!

It is a cuboid or a cube

cone

A pyramid has 5 faces, 5 corners and 8 edges corners and faces are always the same

A cube.

The number of faces determines the bases' shape.

No faces, 1 edge, no corners. A circular disk has 1 face, but that is not the same as a circle.

because if you have the same it would be the same shape.