# 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:

45 | Riemann surface with branch point of order two |

9 | Hyperboloid of one sheet |

24 | Cubic surface with a biplanar double point of *A*_{2} |

1 | Ellipsoid with lines of curvature, an umbillic point can be seen in the upper left |

40 | Catenoid |

33 | Surface of revolution generated by a parabola, with asymptotic curves |

12 | Ellipsoid with confocal hyperboloid with two sheets |

5 | Hyperbolic paraboloid with lines of curvature |

30 | Surface of revolution with constant negative curvature,
conic type |