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cubes, prisms, dodecahedrons...

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Q: Which polyhedron has fewer faces than vertices?
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Which polyhedrons have fewer faces than vertices?

Any polyhedron other than a pyramid.


Which polyhedron has fewer faces than verticies?

Prism.


Which polyhedron has more faces than a tetrahedron but fewer faces than an octahedron?

Hexahedron


Which polyhedron has more faces than a hexahedron but fewer faces than an dodecahedron?

octahedron


Which polyhedron has more faces than an octahedron but fewer faces than an icosahedron?

A dodecahedron


If a polyhedron has 10 more edges than vertices how many faces does it have?

For all polyhedra: vertices + faces = edges + 2 The given fact is: edges = vertices + 10 → vertices + faces = vertices + 10 + 2 → faces = 12


What soild has fewer than 9 vertices?

Tetrahedron- (4 faces, 4 vertices) Octahedron- (8 faces, 6 vertices) Cube- (6 faces, 8 vertices)


Which polyhedron has the fewer number of faces than vertexes?

Any member of the prism family.


What mathematician proved that the sum of the number of faces and vertices of a polyhedron is two more than the number of its edges?

Euler.


How many faces and vertices does a gemstone have with 22 edges?

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.


How many less edges than vertices faces does an octahedron?

According to the Euler characteristic which applies to all simply connected polyhedra,# edges + 2 = # vertices + # faces. So the answer is 2 fewer.


How many vertices and faces of 3D shapes?

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.