Solution to Clues and Coordinates

by David Speyer

The 42 triples of real numbers should be interpreted as three dimensional coordinates. Plotting them in space, solvers will see that they lie on a unit sphere, at regular positions.

More precisely, 12 of the points lie at the vertices of a regular icosahedron, and the remaining 30 points are at the midpoints of the edges of that icosahedron. In the vocabularly of those who build geodesic domes, this is a 2V/L2 geodesic sphere. Taking the convex hull of the points, one obtains a polyhedron with 42 vertices and 80 triangular faces, and a clue associated to each vertex.

Write the answers to the clues in the triangles surrounding the corresponding vertices. Solvers must determine whether each clue cycles clockwise or counter-clockwise, and which triangle it starts in. Here is the resulting grid, shown in a Mercator projection.

Clue (0.2629, 0.8090, -0.5257) reads "What you'll find right above z=0", with the solution ANSWER. Looking a litle above the line of lattitue z=0, solvers will see the word BETELGEUSE.

This puzzle was constructed with the aid of Crux. The author is grateful to Mark Owen (Quinapalus) for his assistance in obtaining and installing Crux.