Any polyhedron other than a pyramid.
Prism.
Any member of the prism family.
Euler.
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.
Any polyhedron other than a pyramid.
Prism.
Hexahedron
octahedron
A dodecahedron
Tetrahedron- (4 faces, 4 vertices) Octahedron- (8 faces, 6 vertices) Cube- (6 faces, 8 vertices)
Oh, dude, it's like a math riddle! So, if a polyhedron has 10 more edges than vertices, we can use Euler's formula: Faces + Vertices - Edges = 2. Since we know the relationship between edges and vertices, we can substitute that in and solve for faces. So, it would have 22 faces. Math can be fun... sometimes.
Any member of the prism family.
Euler.
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.
According to the Euler characteristic which applies to all simply connected polyhedra,# edges + 2 = # vertices + # faces. So the answer is 2 fewer.
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.