a rhombus
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In geometry, a square and a diamond both have four sides. However, the angles are different, and fixed.
"The Diamond Theorem" -- see below -- is described as "... finite projective geometry," showing the number of permutations possible in "... the four-diamond figure as a 4x4 array of two-colour, diagnnally-divided squares."
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few
There are different kinds of geometry including elementary geometry, Euclidean geometry, and Elliptic Geometry.
Archimedes - Euclidean geometry Pierre Ossian Bonnet - differential geometry Brahmagupta - Euclidean geometry, cyclic quadrilaterals Raoul Bricard - descriptive geometry Henri Brocard - Brocard points.. Giovanni Ceva - Euclidean geometry Shiing-Shen Chern - differential geometry René Descartes - invented the methodology analytic geometry Joseph Diaz Gergonne - projective geometry; Gergonne point Girard Desargues - projective geometry; Desargues' theorem Eratosthenes - Euclidean geometry Euclid - Elements, Euclidean geometry Leonhard Euler - Euler's Law Katyayana - Euclidean geometry Nikolai Ivanovich Lobachevsky - non-Euclidean geometry Omar Khayyam - algebraic geometry, conic sections Blaise Pascal - projective geometry Pappus of Alexandria - Euclidean geometry, projective geometry Pythagoras - Euclidean geometry Bernhard Riemann - non-Euclidean geometry Giovanni Gerolamo Saccheri - non-Euclidean geometry Oswald Veblen - projective geometry, differential geometry