Cayley’s Nodal Cubic Surface
A cubic surface is one defined by a polynomial equation of degree 3. Cayley's nodal cubic surface, drawn above by Abdelaziz Nait Merzouk, is the cubic surface with the largest possible number of...
View ArticleKummer Quartic
A quartic surface is one defined by a polynomial equation of degree 4. An ordinary double point is a point where a surface looks like the origin of the cone in 3-dimensional space defined by $x^2 + y^2...
View ArticleTogliatti Quintic
A quintic surface is one defined by a polynomial equation of degree 5. A nodal surface is one whose only singularities are ordinary double points: that is, points where it looks like the origin of the...
View ArticleDiamond Cubic
This picture by Greg Egan shows the pattern of carbon atoms in a diamond, called the diamond cubic. Each atom is bonded to four neighbors. This pattern is found not just in carbon but also other...
View ArticleLaves Graph
This picture by Greg Egan shows the Laves graph, a structure discovered by the crystallographer Fritz Laves in 1932. It is also called the '\(\mathrm{K}_4\) crystal', since is an embedding of the...
View ArticleEscudero Nonic
A nonic surface is one defined by a polynomial equation of degree 9. This image by Juan García Escudero shows a nonic surface called \(Q_9\), which has 220 real ordinary double points: that is, points...
View ArticleBunimovich Stadium
The Bunimovich stadium is a rectangle capped by semicircles in which a point particle moves at constant speed along straight lines, reflecting off the boundary in a way that the angle of incidence...
View ArticleTruncated {6,3,3} Honeycomb
This is an image of the truncated {6,3,3} honeycomb in hyperbolic space.
View ArticleRomik’s Ambidextrous Sofa
The ambidextrous moving sofa problem is to find the planar shape of maximal area that can negotiate right-angled turns both to the right and to the left in a hallway of width 1. The current best known...
View ArticleChmutov Octic
An octic surface is one defined by a polynomial equation of degree 8. This image by Abdelaziz Nait Merzouk shows an octic discovered by Chmutov with 154 real ordinary double points or nodes: that is,...
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