Recognition of Solids
115. The Cube's Perfect Symmetry · Six equal faces, twelve equal edges
A cube has 6 equal square faces and 12 edges of equal length.
A cube is a special cuboid where all 12 edges are equal and all 6 faces are identical squares. Faces, edges, vertices: 6, 12, 8.
What this lesson covers
Try to break it
Try to pull B so one face becomes a rectangle. You can't! By definition, a cube's faces are equal squares. If they change shape, it stops being a cube.
How you build it
Build a cube skeleton from two equal squares.
- Draw the FRONT face square — click the front-top-left corner, then the front-bottom-right.
- Draw the BACK face square — same size locks automatically. Click the back-top-left corner, then click toward the back-bottom-right.
- Draw the depth edge from the front-top-left corner to the back-top-left corner.
- Draw the depth edge from the front-top-right corner to the back-top-right corner.
- Draw the depth edge from the front-bottom-right corner to the back-bottom-right corner.
- Draw the last depth edge from the front-bottom-left to the back-bottom-left corner — cube skeleton complete.
The proof, step by step
Prove that the solid is a cube — all edges equal and all faces squares.
- A cube is a special cuboid where length = breadth = height.
- It has 6 congruent square faces, 12 equal edges, and 8 vertices.
- At each vertex, exactly three edges meet at right angles.
Worked example
A cube has a side length of 5 cm. What is the total length of all its edges combined?
A cube has 12 edges. Total length = 12 × side = 12 × 5 cm = 60 cm.
- 30 cm
- 40 cm
- 60 cm — correct
- 100 cm