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

Table of contents

## Circle

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

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## 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.

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## Rhombus

Rhombus with diagonals $$d_1$$ and $$d_2$$, and side lengths $$a$$.

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## Parallelogram

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

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## Trapezoid

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

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## Sphere

Sphere with radius $$r$$ and diameter $$d$$.

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## Ellipsoid

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

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## Torus

Torus with the radii $$r$$ and $$R$$.

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## Cube

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

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## 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.

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## Straight circular cylinder

A straight cylinder with a height $$h$$ and the radius $$r$$ of its base.

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## 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.

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## Straight circular cone

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

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## Tetrahedron

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

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## Octahedron

Octahedron with side lengths $$a$$. An octahedron has 8 faces and 6 edges.

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## Dodecahedron

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

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