Symmetry & Group Theory:

Group Tables and Subgroup Diagrams

Spirograph Simulators

Finite Simple Group of Order 2

Noam Elkies Colloquium

Change Ringing

Classification of Finite Simple Groups

Numberphile - Monster Group

Hexaflexagon Pattern

4D links:

Unfolding a 4D cube

Slicing a 4D cube

Hypernom game

4D toys app

Tesseract

Miegakure game

The book Flatland

4D Rubik's cube

The regular polychora

All unfoldings of a 4D cube

Tesseract in soap film

Nude Descending a Staircase, No. 2, Marcel Duchamp (1912)

Non-Euclidean geometry links:

Euclid's Elements

Shortest paths on the Earth

Shortest paths on a sphere

Hyperbolic triangle tiling

Hyperbolic plane crochet pattern and exhibit

Poincare disk model

Poincare disk in MC Escher's work

Gauss's great triangle

Henry Segerman's Non-Euclidean VR

Miscellaneous

Mathematically gifted and black

Polyhedron links:

Plato's theory of Platonic solids

Kepler's theory of Platonic solids

Unusual dice from the Dice Lab

Proofs of Euler's formula

Matt Parker's soccer ball petition