Recognition of Solids
66. The Cube's Blueprint · six equal squares, twelve equal edges
All edges of a cube are equal in length, and all faces are identical squares.
A cube is a 3D solid with 6 square faces, 12 equal edges, and 8 vertices. All edges are the same length a and all faces are identical squares of area a². A perfectly regular box.
What this lesson covers
Try to break it
Every edge is exactly the same length. When you drag 'S', all sides stretch together, proving that a cube stays a cube no matter its size!
How you build it
Construct a cube.
- Draw the front face — click corner A, then corner C. The square tool keeps all four sides equal.
- Draw the back face — the same square, shifted diagonally up and to the right.
- Connect the faces — draw the edge AE.
- Draw the connecting edge BF.
- Draw the connecting edge CG.
- Draw the connecting edge DH to complete the cube.
The proof, step by step
Prove that the solid is a cube — six equal square faces.
- A cube has six faces, all of which are identical squares.
- All twelve edges of a cube are equal in length.
- Opposite faces of a cube are parallel and congruent.
Worked example
A cube has 12 edges. If the total length of all edges is 60 cm, what is the length of one edge?
Total edges = 12. Total length = 60 cm. Length of one edge = 60 / 12 = 5 cm.
- 3 cm
- 5 cm — correct
- 10 cm
- 12 cm