In 3D geometry, the number of faces, edges, and vertices of a shape follows Euler's Formula:

$V - E + F = 2$

where:

• $V$ = Number of vertices (corners)
• $E$ = Number of edges (where two faces meet)
• $F$ = Number of faces (flat surfaces)

Common 3D Shapes and Their Properties

3D Shape	Faces (F)	Edges (E)	Vertices (V)
Cube (Square Prism)	6	12	8
Cuboid (Rectangular Prism)	6	12	8
Triangular Prism	5	9	6
Square Pyramid	5	8	5
Triangular Pyramid (Tetrahedron)	4	6	4
Pentagonal Pyramid	6	10	6
Pentagonal Prism	7	15	10
Hexagonal Prism	8	18	12
Octahedron	8	12	6
Dodecahedron	12	30	20
Icosahedron	20	30	12
Cylinder	3	2	0
Cone	2	1	1
Sphere	1	0	0

Would you like a detailed explanation for any specific shape?

Related Questions

1. How does Euler’s formula work for different 3D shapes?
2. Why does a sphere have 0 edges and 0 vertices?
3. How do you calculate faces, edges, and vertices for irregular polyhedra?
4. What are the differences between prisms and pyramids in terms of faces, edges, and vertices?
5. How can we use 3D nets to count faces, edges, and vertices?

🔢 Tip: To check Euler’s formula for any shape, use $V - E + F = 2$ and see if it holds! 🚀