This list includes these: It was proven in Sopov (1970) that there are only 75 uniform polyhedra other than the infinite families of prisms and antiprisms.
John Skilling discovered an overlooked degenerate example, by relaxing the condition that only two faces may meet at an edge.
The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively.
The convex forms are listed in order of degree of vertex configurations from 3 faces/vertex and up, and in increasing sides per face.
423, 425, 426; Skilling 1975, p. 123) The great disnub dirhombidodecahedron has 240 of its 360 edges coinciding in space in 120 pairs.