3D Shapes & Net Explorer
Visualise and describe 3D objects by their faces, edges, and vertices. Master the key 3D shapes and identify their nets for 11+ papers.
3D Shapes
11+ Mathematics Topic Guide
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What you'll learn
4 core skill areas across this topic
Interactive 3D Shape Explorer
Rotate and study properties of common 3D shapes in interactive way !
A cube is the only regular hexahedron — all 6 faces are identical squares.
F + V − E = 6 + 8 − 12 = 2Choose a shape
11+ Tip
Euler's Formula checks your answers: F + V − E = 2 holds for all prisms and pyramids. If your answer doesn't satisfy this, double-check!
Common Prisms
Prisms have a uniform cross-section and flat rectangular sides
✨ Constant Cross-Section: No matter where you cut it parallel to the ends, the shape remains the same.
✨ Identical Ends: A prism has two identical flat ends (called bases) connected by rectangular sides.
✨ Not a Prism: A cylinder is not a prism because it has a curved surface, not flat polygonal sides.
🐝 Fun Fact: Honeycombs are incredibly efficient hexagonal prisms built naturally by bees.
Pyramids
All sides meet at a single shared vertex (the apex)
✨ Sides Always Triangles: No matter the base, the sides of a pyramid are always triangles.
✨ Named by Bases: Named after their base shape; a triangular pyramid has a triangle on the bottom.
✨ Vertex vs. Apex: The corners where edges meet are vertices, but the single top point is the apex.
🏛️ Fun Fact: The Great Pyramid of Giza is a square-based pyramid, built over 4,500 years ago!
Note: A tetrahedron is a pyramid with a triangular base — it has the fewest faces of any polyhedron!
Curved 3D Shapes
Solids with at least one curved surface
Spheres, cones & cylinders do notfollow Euler's Formula because they have curved surfaces.
Nets of a Cube
Analyse the 11 unique ways to flatten a cube into a 2D pattern
Net of Cube Interactive
Classification: 1-4-1
Pattern 1 (Cross)
The classic symmetrical cross pattern.
Opposite faces share a color to help you track them while folding.
Nets in the 1-4-1 group belong to the 11 unique ways to form a cube.
Faces separated by exactly one square in a row will always be opposite in 3D.
Unique Patterns
There are exactly 11 ways a cube can be unfolded. In the 11+ exam, you often have to spot which patterns *cannot* form a cube.
Opposite Faces
Faces separated by exactly one square in a straight line on the net will always be **opposite** to each other in 3D.
The 11 Nets of a Cube
Primary Color Pairs Guide
1 square on left, 4 in center, 1 square on right
1 sq left, 3 center, 2 on right
3-3 Staircase and 2-2-2 Zig-Zag
💡 Faces of the same color will always be opposite in 3D!
Nets of Other Solid Shapes
Identify the patterns for pyramids, prisms, and curved solids
Square-based Pyramid
Triangular Prism
Tetrahedron
Cylinder
Key facts to remember
All prisms have a constant cross-section throughout their length
Euler’s formula (Faces + Vertices − Edges = 2) works for all convex polyhedra (no curves!)
A cube can have 11 different 2D nets
A sphere has no edges and no vertices
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