The 16 most Important Geometric Objects: Overview with Formulas and Properties
Table of contents
- Circle
- Isosceles Triangle
- Rhombus
- Parallelogram
- Trapezoid Flat quadrilateral with two sides parallel to each other.
- Sphere
- Ellipsoid
- Torus
- Cube
- Cuboid A cuboid is bounded by 6 rectangles.
- Straight circular cylinder
- Straight circular truncated cone
- Straight circular cone
- Tetrahedron
- Octahedron
- Dodecahedron
Circle
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
Isosceles triangle with base \(a\) and height \(h\). An isosceles triangle has at least two sides of equal length and two equal angles.
Rhombus
Rhombus with diagonals \(d_1\) and \(d_2\), and side lengths \(a\).
Parallelogram
Parallelogram with side lengths \(a\) and \(b\), and corresponding angles \(\alpha\) and \(\beta\) and height \(h\).
Trapezoid
A trapezoid with height \(h\) and side lengths \(a\) and \(b\) is a plane quadrilateral with two sides parallel to each other.
Sphere
Sphere with radius \(r\) and diameter \(d\).
Ellipsoid
Ellipsoid with three semi-axes \(a\), \(b\), and \(c\), which are generally of different lengths.
Torus
Torus with the radii \(r\) and \(R\).
Cube
A cube has 6 sides, 12 sides of equal length and 8 edges. The side length is \(a\).
Cuboid
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.
Straight circular cylinder
A straight cylinder with a height \(h\) and the radius \(r\) of its base.
Straight circular truncated cone
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
Straight circular cone with height \(h\), radius \(r\) of circular base and side length \(s\).
Tetrahedron
Tetrahedron (regular polyhedron, Platonic solid) with side lengths \(a\). A tetrahedron has 4 faces and 4 corners.
Octahedron
Octahedron with side lengths \(a\). An octahedron has 8 faces and 6 edges.
Dodecahedron
A dodecahedron has 12 faces, 20 edges and is one of the five Platonic solids. Its side length is \(a\).
