List of convex regular-faced polyhedra explained

This is a list of convex, regular-faced polyhedra. Since there are an infinite number of prisms and antiprisms, only a few have been listed.

Name	Platonic?	Archimedean?	Prism?	Antiprism?	Pyramid?	Dipyramid?	Deltahedron?	Faces (3)	Faces (4)	Faces (5)	Faces (6)	Faces (8)	Faces (10)	Faces (12)	Faces (n)	Edges	Vertices
Tetrahedron	Yes	No	No	No	Yes	No	Yes	4	0	0	0	0	0	0	-	6	4
Cube	Yes	No	Yes	No	No	No	No	0	6	0	0	0	0	0	-	12	8
Octahedron	Yes	No	No	Yes	No	Yes	Yes	8	0	0	0	0	0	0	-	12	6
Dodecahedron	Yes	No	No	No	No	No	No	0	0	12	0	0	0	0	-	30	20
Icosahedron	Yes	No	No	No	No	No	Yes	20	0	0	0	0	0	0	-	30	12
Truncated tetrahedron	No	Yes	No	No	No	No	No	4	0	0	4	0	0	0	-	18	12
Cuboctahedron	No	Yes	No	No	No	No	No	8	6	0	0	0	0	0	-	24	12
Truncated cube	No	Yes	No	No	No	No	No	8	0	0	0	6	0	0	-	36	24
Truncated octahedron	No	Yes	No	No	No	No	No	0	6	0	8	0	0	0	-	36	24
Rhombicuboctahedron	No	Yes	No	No	No	No	No	8	18	0	0	0	0	0	-	48	24
Great rhombicuboctahedron	No	Yes	No	No	No	No	No	0	12	0	8	6	0	0	-	72	48
Snub cube	No	Yes	No	No	No	No	No	32	6	0	0	0	0	0	-	60	24
Icosidodecahedron	No	Yes	No	No	No	No	No	20	0	12	0	0	0	0	-	60	30
Truncated dodecahedron	No	Yes	No	No	No	No	No	20	0	0	0	0	12	0	-	90	60
Truncated icosahedron	No	Yes	No	No	No	No	No	0	0	12	20	0	0	0	-	90	60
Rhombicosidodecahedron	No	Yes	No	No	No	No	No	20	30	12	0	0	0	0	-	120	60
Great rhombicosidodecahedron	No	Yes	No	No	No	No	No	0	30	0	20	0	12	0	-	180	120
Snub dodecahedron	No	Yes	No	No	No	No	No	80	0	12	0	0	0	0	-	150	60
Triangular prism	No	Yes	Yes	No	No	No	No	2	3	0	0	0	0	0	-	9	6
Pentagonal prism	No	Yes	Yes	No	No	No	No	0	5	2	0	0	0	0	-	15	10
Octagonal prism	No	Yes	Yes	No	No	No	No	0	8	0	0	2	0	0	-	24	16
n-prism	No	Yes	Yes	No	No	No	No	-	n	-	-	-	-	-	2	3n	2n
Square antiprism	No	Yes	No	Yes	No	No	No	8	2	0	0	0	0	0	-	16	8
Pentagonal antiprism	No	Yes	No	Yes	No	No	No	10	0	2	0	0	0	0	-	20	10
n-antiprism	No	Yes	No	Yes	No	No	No	2n	-	-	-	-	-	-	2	4n	2n
Square pyramid	No	No	No	No	Yes	No	No	4	1	0	0	0	0	0	-	8	5
Pentagonal pyramid	No	No	No	No	Yes	No	No	5	0	1	0	0	0	0	-	10	6
Triangular cupola	No	No	No	No	No	No	No	4	3	0	1	0	0	0	-	15	9
Square cupola	No	No	No	No	No	No	No	4	5	0	0	1	0	0	-	20	12
Pentagonal cupola	No	No	No	No	No	No	No	5	5	1	0	0	1	0	-	25	15
Pentagonal rotunda	No	No	No	No	No	No	No	10	0	6	0	0	1	0	-	35	20
Gyroelongated pentagonal pyramid	No	No	No	No	No	No	No
Triangular dipyramid	No	No	No	No	No	Yes	Yes
Pentagonal dipyramid	No	No	No	No	No	Yes	Yes
Gyroelongated square dipyramid	No	No	No	No	No	No	Yes
Elongated square cupola	No	No	No	No	No	No	No
Elongated square gyrobicupola	No	No	No	No	No	No	No	8	18	0	0	0	0	0	-	48	24
Triaugmented triangular prism	No	No	No	No	No	No	Yes
Metabidiminished icosahedron	No	No	No	No	No	No	No
Tridiminished icosahedron	No	No	No	No	No	No	No
Diminished rhombicosidodecahedron	No	No	No	No	No	No	No
Parabidiminished rhombicosidodecahedron	No	No	No	No	No	No	No
Metabidiminished rhombicosidodecahedron	No	No	No	No	No	No	No
Tridiminished rhombicosidodecahedron	No	No	No	No	No	No	No
Snub disphenoid	No	No	No	No	No	No	Yes
Snub square antiprism	No	No	No	No	No	No	No
Sphenocorona	No	No	No	No	No	No	No
Sphenomegacorona	No	No	No	No	No	No	No
Hebesphenomegacorona	No	No	No	No	No	No	No
Disphenocingulum	No	No	No	No	No	No	No
Bilunabirotunda	No	No	No	No	No	No	No
Triangular hebesphenorotunda	No	No	No	No	No	No	No