Q: Does all 3d shapes have vertices?

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There are an infinite number of 3d shapes. For example you can have an infinite number of prisms with ends that are triangular, quadrilateral, or in the shape of any polygon.

sphere

vertice is just a scientific word for corner

cubes and rectangular prisms

According to Euler none; for all 3d shapes: Vertices + Faces = Edges + 2 ⇒ 12 + 8 = 19 + 2 ⇒ 20 = 21 So unless 20 does equal 21, no 3d shape has 8 faces, 19 edges and 12 vertices. Any 3d shape with 8 faces would be an octahedron.

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There are an infinite number of 3d shapes. For example you can have an infinite number of prisms with ends that are triangular, quadrilateral, or in the shape of any polygon.

sphere

vertice is just a scientific word for corner

You can find a polyhedron with any number greater than 4 of vertices or faces. However, a torus, ellipsoid, sphere, paraboloid, hyperboloid are all standard shapes with no vertices. Cylinders, too, have no vertices. And there are many completely random shapes - a lump of putty, for example, which will have no vertex.

1. A cube & 2. A rectangular prism

A cube has 6 faces

cubes and rectangular prisms

For two dimensional shapes, a vertex (plural vertices) is a point where two sides meet.For 3D shapes, a vertex is a point where three or more faces meet.

Yes Vertex(Vertices) are corners or points of 3D shapes.

According to Euler none; for all 3d shapes: Vertices + Faces = Edges + 2 ⇒ 12 + 8 = 19 + 2 ⇒ 20 = 21 So unless 20 does equal 21, no 3d shape has 8 faces, 19 edges and 12 vertices. Any 3d shape with 8 faces would be an octahedron.