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The Anatomy of 3D Shapes

Every time you roll a standard dice, you are interacting with faces, edges, and vertices. To accurately describe three-dimensional solids in geometry, you must use precise terminology to identify their different parts.

A face is a single flat surface of a 3D shape. This term is primarily used for solids with flat sides, though it also applies to the flat circular bases of cylinders and cones.
A surface refers to the entire exterior boundary of an object. In OCR exams, you must specifically use the term "curved surface" to describe the non-flat, rounded parts of objects like spheres and cylinders.
An edge is the line segment or curve where two faces or surfaces meet. Edges can be perfectly straight lines or curved rings.
A vertex (plural: vertices) is a point or "corner" where three or more edges meet.
An apex is a specific type of vertex found at the very top of a cone or a pyramid.

Polyhedra: Solids with Flat Faces

Polyhedra are 3D solids constructed entirely from flat faces and straight edges. Identifying their properties is key to distinguishing between them.

A cube has 6 congruent square faces, 12 equal-length edges, and 8 vertices. All of its interior angles meet at exactly $90^\circ$ .

Students frequently confuse edges with vertices; remember that edges are the long lines connecting corners, while vertices are the pointy corners themselves.

In OCR mark schemes, precision is critical: always use the phrase 'curved surface' rather than 'face' when referring to the rounded exteriors of cylinders, cones, and spheres.

When naming a prism in an exam, always identify it by the shape of its cross-section (e.g., 'triangular prism' rather than just 'prism') to secure full marks.

Remember the OCR specific alignments for vertices on curved solids: a cylinder has strictly 0 vertices, whilst a cone has exactly 1 vertex.

A single flat surface of a three-dimensional solid.

The outer boundary of a 3D object, often used specifically to describe curved areas.

The straight line or curve where two faces or surfaces meet.

A corner or point on a 3D solid where three or more edges meet.

The specific vertex at the highest point of a cone or pyramid.

A 3D solid that is made up exclusively of flat faces and straight edges.

A 3D solid that has a constant two-dimensional cross-section running through its entire length.

A prism with two congruent triangular bases and three rectangular side faces.

A 3D solid with a polygonal base and flat triangular faces that converge at a single apex.

A pyramid with a square base and four triangular side faces meeting at an apex.

A polyhedron consisting of 6 congruent square faces, 12 edges, and 8 vertices.

A polyhedron with 6 rectangular faces, where opposite faces are congruent, possessing 12 edges and 8 vertices.

A pyramid with a triangular base, consisting of 4 triangular faces, 6 edges, and 4 vertices.

A 3D solid with two flat circular bases and one curved surface connecting them.

A 3D solid featuring one flat circular base, one curved surface, and exactly one vertex.

A perfectly round 3D solid consisting of a single continuous curved surface with no flat faces, edges, or vertices.