Faces, Edges and Vertices of Polyhedron

Have you ever wondered what makes a dice different from a ball, or why a soda can holds so much more than a box of the same height? The answer lies in Solid Geometry, the study of three-dimensional (3D) objects.

3D shapes have length, width, and height, giving them volume and allowing them to take up space in the real world. Understanding them is crucial, as they form the foundation for architecture, engineering, packaging, and even video game design.

A cube is a special type of cuboid where all sides are equal. It is a symmetrical three-dimensional shape with:

• Faces: 6 square faces (ABCD, ABFE, AEHD, CGHD, CGFB, and EFGH)

• Edges: 12 edges (AB, BC, CD, DA, AE, EH, HD, EF, FG, GH, BF and CG)

• Vertices: 8 corners (A, B, C, D, E, F, G, and H)

All faces are congruent (equal) squares, making length = breadth = height.

A cube is a special type of cuboid where all sides are equal. It is a symmetrical three-dimensional shape with:

• Faces: 6 square faces (ABCD, ABFE, AEHD, CGHD, CGFB, and EFGH)

• Edges: 12 edges (AB, BC, CD, DA, AE, EH, HD, EF, FG, GH, BF and CG)

• Vertices: 8 corners (A, B, C, D, E, F, G, and H)

All faces are congruent (equal) squares, making length = breadth = height.

Has two equal circular ends and one curved surface.

• Faces: S₁ (top), S₂ (bottom), S₃ (curved)

• Edges: Two circular edges

• Vertices: None

A sphere is a perfectly round solid where every point on its surface is equidistant from its center. It has:

• Faces: 1 curved surface

• Edges: 0 edges

• Vertices: 0 vertices

The sphere is unique among 3D solids because it has no flat faces, edges, or corners—only a single continuous curved surface.

A cone is a solid that tapers from a circular base to a single point called the vertex (or apex). It consists of:

• Faces: 2 surfaces (one circular base S2 and one curved surface S1)

• Edges: 1 curved edge

• Vertices: 1 vertex

The cone has one flat circular face at the bottom and a curved surface that narrows to a point at the top.

Has two triangular bases and three rectangular face

• Faces: 3 side faces (AA'C'C, ABB'A', and BB'C'C) plus 2 triangular end faces (ABC and A'B'C')

• Edges: 9 edges (AB, AC, BC, A'B', A'C', B'C', AA', BB', and CC')

• Vertices: 6 vertices (A, B, C, A', B', and C')

The two triangular end faces are always parallel and congruent.

Has two triangular bases and three rectangular faces.

• Faces: 4 triangular faces (triangular base ABC and three side faces PAB, PBC, and PAC)

• Edges: 6 edges

• Vertices: 4 vertices (including vertex P, the apex)

Has a quadrilateral base ABCD

• Faces: 5 faces (quadrilateral base ABCD and four triangular side faces ΔPAB, ΔPBC, ΔPCD, and ΔPDA)

• Edges: 8 edges

• Vertices: 5 vertices (including vertex P, the apex)