3D Solids: Polyhedra vs. Non-Polyhedra
3D Solids: Polyhedra vs. Non-Polyhedra is a Grade 7-8 geometry skill that teaches students to classify three-dimensional figures. Polyhedra have flat polygonal faces only (like prisms and pyramids), while non-polyhedra have curved surfaces (like spheres, cylinders, and cones).
Key Concepts
Property Geometric solids are 3D figures that have length, width, and depth. Polyhedron: A specific type of solid where ALL faces are flat polygons, meaning it has zero curved surfaces. Non Polyhedron: A 3D figure that contains at least one curved surface.
Examples Cube: A polyhedron with 6 identical square faces. Cylinder & Cone: Non polyhedra because they have curved surfaces connecting to circular bases. Sphere: A perfectly round solid with no flat faces at all.
Explanation Think of it this way: a drawing on paper is flat, but a book is a 3D solid you can actually hold. If a 3D shape is completely blocky and flat on every side, it is a polyhedron. If it can roll smoothly on the floor (like a soup can or a party hat), it has curves and is a non polyhedron!
Common Questions
What is a polyhedron?
A polyhedron is a 3D solid with only flat polygonal faces. Examples include cubes, rectangular prisms, triangular prisms, and pyramids.
What is a non-polyhedron?
A non-polyhedron is a 3D solid with at least one curved surface. Examples include spheres, cylinders, and cones.
Is a cylinder a polyhedron?
No, a cylinder is not a polyhedron because it has curved surfaces (the lateral face). Polyhedra must have only flat faces.
What are examples of polyhedra?
Cube, rectangular prism, triangular prism, square pyramid, triangular pyramid (tetrahedron), and other prisms and pyramids.
What grade covers polyhedra vs. non-polyhedra?
Classifying 3D solids as polyhedra and non-polyhedra is covered in Grade 7 and Grade 8 geometry.