Hasse diagram

English: A Hasse diagram is a graphical representation of a partially ordered set.

Misc.

Subsets of a 2-element set			Subsets of a 3-element set			Divisors of 60 ordered by divisibility			Non-negative integers ordered by divisibility
Young–Fibonacci lattice			Young's lattice			Left: Divisors of 120 ordered by divisibility (Birkhoff's representation theorem)
Associahedron of order 4				Permutohedron of order 4				Lattice of regular bands
Free distributive lattices of monotonic Boolean functions				Rieger–Nishimura lattice (free Heyting algebra over one generator)				Types of quadrilaterals

Tesseract

Subsets of a 4-element set:

Emphasis on two cubes	Rhombic dodecahedral parallel projection of the tesseract	Logical connectives
Emphasis on all eight cubes	4x4 matrix	Tetrahedral central projection of the tesseract Not a Hasse diagram, but similar: Highest element in center; lower elements farer away from center; lowest element not shown

Set partitions

Partitions of a 4-element set ordered by refinement:

		Only the 14 noncrossing partitions (This diagram is also vertically symmetric.)
Emphasis on sublattice	Emphasis on symmetry	Emphasis on number of elements per rank

Lattice of subgroups

Dihedral group Dih4	Z23	Z24 (rank expressed by background color, not by position)
30 subgroups of S4	9 types of subgroups of S4	25 types of subgroups of the S4 × C2

First-order logic

v:Formulas in predicate logic

Root systems

A7

C5

F4