Solution to Showcase

by David Speyer

The flavor text should bring solvers to Building 2, and should also clue them that this puzzle works modulo 26. On the first floor of building 2, near the entrance to Killian Court, there is a glass showcase filled with mathematical models.

(this and other photos useful in the writing of this puzzle taken by Andrew Thomas)

Identify the model corresponding to each clue, and take the number of the model modulo 26. The equations given are not precise matches for the objects, but they are reasonably close, and they always match exactly the descriptions on the placards. I don't always clue all the details on every object, but I clue enough to be completely disambiguating. Using the familiar A=1, B=2, etc code, this spells SIX-ANGLED, cluing the answer HEXAGONAL.

The models are:

45Riemann surface with branch point of order two
9Hyperboloid of one sheet
24Cubic surface with a biplanar double point of A2
1Ellipsoid with lines of curvature, an umbillic point can be seen in the upper left
33Surface of revolution generated by a parabola, with asymptotic curves
12Ellipsoid with confocal hyperboloid with two sheets
5Hyperbolic paraboloid with lines of curvature
30Surface of revolution with constant negative curvature, conic type