The 16 most Important Geometric Objects: Overview with Formulas and Properties

Circle with radius \(r\). Circles occur everywhere in physics, for example in a circular motion or when particles move in a magnetic field.

Isosceles triangle with base \(a\) and height \(h\). An isosceles triangle has at least two sides of equal length and two equal angles.

Rhombus with diagonals \(d_1\) and \(d_2\), and side lengths \(a\).

Parallelogram with side lengths \(a\) and \(b\), and corresponding angles \(\alpha\) and \(\beta\) and height \(h\).

A trapezoid with height \(h\) and side lengths \(a\) and \(b\) is a plane quadrilateral with two sides parallel to each other.

Sphere with radius \(r\) and diameter \(d\).

Ellipsoid with three semi-axes \(a\), \(b\), and \(c\), which are generally of different lengths.

Torus with the radii \(r\) and \(R\).

A cube has 6 sides, 12 sides of equal length and 8 edges. The side length is \(a\).

A cuboid is a geometric solid bounded by 6 rectangles. A cuboid has 6 rectangular side faces that are at right angles to each other, 8 right-angled edges, and 12 sides, four of which have equal lengths and are parallel to each other.

A straight cylinder with a height \(h\) and the radius \(r\) of its base.

Truncated cone with round bases. The truncated cone has height \(h\), side length \(s\), radius \(r_1\) of the lower circular base and radius \(r_2\) of the upper circular base.

Straight circular cone with height \(h\), radius \(r\) of circular base and side length \(s\).

Tetrahedron (regular polyhedron, Platonic solid) with side lengths \(a\). A tetrahedron has 4 faces and 4 corners.

Octahedron with side lengths \(a\). An octahedron has 8 faces and 6 edges.

A dodecahedron has 12 faces, 20 edges and is one of the five Platonic solids. Its side length is \(a\).