A plane of symmetry divides a solid into mirror-image halves. An axis of rotational symmetry is a line about which a turn leaves the solid in the same position. Its order counts the matching positions in one full turn, including the starting position. Example A right square-based pyramid has four vertical symmetry planes. Its main axis joins the apex to the centre of the base and has rotational order 4. **Solid** | **Planes of symmetry** | **Rotation about its main axis** Right circular cylinder | Every plane through the axis, and the mid-plane perpendicular to it | Any angle Right circular cone | Every plane through the axis | Any angle Right prism with a regular n-gon base | n longitudinal planes and the mid-plane perpendicular to the length | Order n A cone has no horizontal plane of symmetry: reflecting the apex would not reproduce the base. Specify the axis under discussion; a solid can have other rotational axes as well.

A plane of symmetry divides a solid into mirror-image halves. An axis of rotational symmetry is a line about which a turn leaves the solid in the same position. Its order counts the matching positions in one full turn, including the starting position.

A right square-based pyramid has four vertical symmetry planes. Its main axis joins the apex to the centre of the base and has rotational order 4.

A cone has no horizontal plane of symmetry: reflecting the apex would not reproduce the base. Specify the axis under discussion; a solid can have other rotational axes as well.

Polygons

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Planes and axes of symmetry

Planes and axes of symmetry

Solid	Planes of symmetry	Rotation about its main axis
Right circular cylinder	Every plane through the axis, and the mid-plane perpendicular to it	Any angle
Right circular cone	Every plane through the axis	Any angle
Right prism with a regular n-gon base	n longitudinal planes and the mid-plane perpendicular to the length	Order n