The dodecahedral conjecture in geometry is intimately related to sphere packing. László Fejes Tóth, a 20th-century Hungarian geometer, considered the...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

honeycomb conjecture The most efficient partition of the plane into equal areas is the regular hexagonal tiling. Related to Thue's theorem. Dodecahedral conjecture...

1998, Shou-Wu Zhang, 1998) Kepler conjecture (Samuel Ferguson, Thomas Callister Hales, 1998) Dodecahedral conjecture (Thomas Callister Hales, Sean McLaughlin...

In mathematics, Thurston's geometrization conjecture (now a theorem) states that each of certain three-dimensional topological spaces has a unique geometric...

The rhombic dodecahedral honeycomb (also dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram...

rational coefficients. The Poincaré homology sphere (also known as Poincaré dodecahedral space) is a particular example of a homology sphere, first constructed...

hyperbolic 3-manifold. It is also known as Seifert–Weber dodecahedral space and hyperbolic dodecahedral space. It is one of the first discovered examples of...

hyperbolic 3-manifold. It is also known as Seifert–Weber dodecahedral space and hyperbolic dodecahedral space. It is one of the first discovered examples of...

(Harvey Mudd College) 1999 Winner: Sean McLaughlin (Proof of the Dodecahedral Conjecture, University of Michigan) Honorable mention: Samit Dasgupta (Harvard...

{\displaystyle c_{5}} were prime, it would also contradict the New Mersenne conjecture. It is known that 2 c 4 + 1 3 {\displaystyle {\frac {2^{c_{4}}+1}{3}}}...

conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture was...

tetrahedral number, the sum of the first ten triangular numbers, and a dodecahedral number. If all of the diagonals of a regular decagon are drawn, the resulting...

2D Euclidean space. Its three dimensional equivalent is the rhombic dodecahedral honeycomb, derived from the most dense packing of spheres in 3D Euclidean...

. {\displaystyle 2k.} Andrica's conjecture, Brocard's conjecture, Legendre's conjecture, and Oppermann's conjecture all suggest that the largest gaps...

finite subdivision rules as an attempt to prove the following conjecture: Cannon's conjecture: Every Gromov hyperbolic group with a 2-sphere at infinity...

problem in mathematics: Are any Fortunate numbers composite? (Fortune's conjecture) (more unsolved problems in mathematics) A Fortunate number, named after...

graph – 8 vertices, 12 edges Icosahedral graph – 12 vertices, 30 edges Dodecahedral graph – 20 vertices, 30 edges A polyhedral graph is the graph of a simple...

corollary of the Kepler conjecture: it can be achieved by putting a rhombicuboctahedron in each cell of the rhombic dodecahedral honeycomb, and it cannot...

and 8191 (111 in base-90, 1111111111111 in base-2). The Goormaghtigh conjecture says there are only these two cases. Using the pigeon-hole principle it...

top and bottom cuts. A space-filling tessellation, the trapezo-rhombic dodecahedral honeycomb, can be made by translated copies of this cell. Each "layer"...

according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them. There are infinitely many lucky numbers. Twin...

Sierpiński number. In private correspondence with Paul Erdős, Selfridge conjectured that 78,557 was the smallest Sierpiński number. No smaller Sierpiński...

can be less than 16. In his 1981 thesis, Alan R. Woods independently conjectured that whenever k > 1, the interval [a, a + k] always includes a number...

pp. 100–101. (The full text can be found at ProofWiki: Catalan-Dickson Conjecture.) Bratley, Paul; Lunnon, Fred; McKay, John (1970). "Amicable numbers and...

Because no covering set has been found for any k less than 509203, it is conjectured to be the smallest Riesel number. To check if there are k < 509203, the...

corollary of the Kepler conjecture: it can be achieved by putting a rhombicuboctahedron in each cell of the rhombic dodecahedral honeycomb, and it cannot...

The trapezo-rhombic dodecahedron, the prototile of the trapezo-rhombic dodecahedral honeycomb and the plesiohedron generated by the hexagonal close-packing...

Frederick Pollock conjectured that every natural number is the sum of at most eleven centered nonagonal numbers. Pollock's conjecture was confirmed as...

Frederick Pollock conjectured that every positive integer is the sum of at most 5 tetrahedral numbers: see Pollock tetrahedral numbers conjecture. The only tetrahedral...