Polyhedron and Polyhedra Vol.2 vs Millennium Problems

Polyhedron and Polyhedra Volume 2 is a collection of 4 kepler-poinsot polyhedra, 53 uniform star polyhedra, their duals and polyhedral compounds of them. This is also an application which helps you to learn about or explore these mathematical solids. Without knowledge of mathematics or polyhedron, you can easily interact with the 3d solids by this application. So, you will become more familiar with the polyhedrons, and you may enjoy these abstract solids as fascinating formative arts. The main advantage of this app is that it offers a large variety of polyhedral compounds of identical uniform star polyhedra and their duals. By choosing a model, and by setting colors and parameters optionally, you will find various types of 3d shapes including wonderful shapes, mysterious artistic shapes, and strange eccentric shapes, which will be interesting for you. Features: - Swipe or touch gesture will rotate, zoom or move the object. So, you can observe it from various angles or positions. (You can observe it even from inside.) - Switches between showing and hiding each face of the polyhedron, and switches between showing and hiding each component of the compound - Function to display the edges of the polyhedra with selectable thickness and color - For each kepler-poinsot polyhedron, each uniform star polyhedron and each dual of uniform star polyhedron, the app can provide the compound from 14 to 22 kinds (more than 1200 in total). - Many color patterns for the faces of the polyhedron. - Functions to display basic informations about the polyhedron, and to access the wikipedia sites about the related items - Slider controllers to reduce z-fighting (screen flicker) - Save PNG images to camera roll

Can you solve a problem worth $1,000,000? The Clay Mathematics Institute has offered a million-dollar prize for each of seven unsolved mathematical problems — and nobody has claimed them yet. Millennium Problems brings these mysteries to life for everyone, from curious 11-year-olds to doctoral researchers. SEVEN LEGENDARY PROBLEMS • P vs NP — Is finding as hard as checking? • Riemann Hypothesis — Where do prime numbers hide? • Yang-Mills & Mass Gap — Why do particles have mass? • Navier-Stokes — Can we predict turbulent fluids? • Hodge Conjecture — What shapes are built from algebra? • Birch & Swinnerton-Dyer — How many solutions does an equation have? • Poincaré Conjecture — The shape of the universe (SOLVED!) EVERY SKILL LEVEL Choose your grade — from Grade 6 to Graduate — and the content adapts instantly. The same problem is explained with simple analogies for a middle schooler and rigorous proofs for a PhD student. INTERACTIVE 3D VISUALISATIONS Every problem comes with a real-time Three.js visualisation. Watch elliptic curves rotate, Riemann zeros appear on the critical line, and fluid particle fields swirl — all rendered natively on your device. BUILT-IN QUIZZES Test your understanding with 5 questions per problem per grade level. Earn XP, track your streak, and collect badges as you explore. WORKS OFFLINE No account. No subscription. No ads. Everything runs locally on your device. OPTIONAL BIOMETRIC LOCK Protect your progress with Face ID, Touch ID, or fingerprint — entirely optional. Whether you're a student looking for a challenge, a teacher seeking engaging material, or a mathematician revisiting the classics, Millennium Problems meets you where you are. Clay Mathematics Institute · $7,000,000 in unclaimed prizes · Since 2000