# 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 \(a\).