Solids-3D

List of Geometrics Shapes - 3D Shapes

Here are some common 3D shapes that you should know.

Along with a picture of each shape, the number of faces, edges and vertices are also given.

Common properties of the 3D shapes are also given.

Please note that there is some disagreement over the definitions and properties of 3d shapes.

Some mathematicians allow a face to be curved and some do not.

Some mathematicians allow an edge to be curved and some do not.

Cube	Cubes have 6 faces, 12 edges and 8 vertices. All sides on a cube are equal length. All faces are square in shape. A cube is a type of cuboid.
Cuboid	Cuboids have 6 faces, 12 edges and 8 vertices. All the faces on a cuboid are rectangular.
Sphere $3d geometric shapes sphere$	Spheres have either 0 or 1 faces, 0 edges and 0 vertices.
Ellipsoid $3d geometric shapes ellipsoid$	Ellipsoids have either 0 or 1 faces, 0 edges and 0 vertices.
Cylinder	Cylinders have either 2 or 3 faces, 0 or 2 edges, and 0 vertices.
Cone	Cones have either 1 or 2 faces, 0 or 1 edges, and 1 apex (which is described by some mathematicians as a vertex).
Triangular Prism	Triangular Prisms have 5 faces, 9 edges, and 6 vertices. The two faces at either end are triangles, and the rest of the faces are rectangular.
Hexagonal Prism	Hexagonal Prisms have 8 faces, 18 edges, and 12 vertices. The two faces at either end are hexagons, and the rest of the faces are rectangular.
Triangular-based Pyramid	Triangular-based pyramids have 4 faces, 6 edges and 4 vertices. The base is a triangle. All of the faces are triangular. If the triangular faces making up the prism are all equilateral, then the shape is also called a Tetrahedron.
Square-based Pyramid	Square based pyramids have 5 faces, 8 edges and 5 vertices The base is a square. All the other faces are triangular.
Hexagonal Pyramid	Hexagonal pyramids have 7 faces, 12 edges, and 7 vertices. The base is a hexagon. All of the other faces are triangular.

The 5 Platonic Solids

The platonic solids form a set of 5 polyhedra with the following special properties:

They are named after the Greek philosopher Plato who wrote about them in his philosophical discussions.

There are only 5 platonic solids:

Tetrahedron $tetrahedron$	A Tetrahedrons is the same as a triangular pyramid. They have 4 triangular faces, 6 edges and 4 vertices. A regular tetrahedron has equilateral triangles for its faces, and is one of the 5 platonic solids.
Cube (regular hexahedron)	Cubes have 6 faces, 12 edges and 8 vertices. All sides on a cube are equal length. All faces are square in shape. A cube is a type of cuboid and is one of the 5 platonic solids.
Octahedron $3 d shapes octahedron$	Octahedrons are a shape with 8 faces, 12 edges and 6 vertices. A regular octahedron has equilateral triangles for its faces, and is one of the 5 platonic solids.
Dodecahedron $printable 3d shapes dodecahedron$	Dodecahedrons are a shape with 12 faces, 30 edges and 20 vertices. A regular dodecahedron has regular pentagons for its faces, and is one of the 5 platonic solids.
Icosahedron $printable 3d shapes icosahedron$	Icosahedron are a shape with 20 faces, 30 edges and 12 vertices. All the faces are triangles. A regular icosahedron is one of the 5 platonic solids with all faces being equilateral triangles.