This family of design variations are all stellated variation of Stewart Coffin's "Jupiter" puzzle. In addition to the stellation itself, I've made some aesthetic tweaks to the shape of the pieces in order to give it an organic feeling, somewhat inspired by Ernst Haeckel's 1904 lithograph "Blastoidea" which depicts various members of the sea urchin family.

From a strictly geometric perspective, all 12 pieces of each version have the same 5-fold rotationally symmetric shape as each other. Assembly is tricky to figure out at first if you're not familiar with this kind of puzzle, yet it's not especially difficult to do once you've done it a few times. There are a few fun Ah-Ha moments in this process which include elements of sequence and dexterity challenges.

Coffin's Classic 6-color system (dodecahedral symmetry)

The true beauty and puzzling challenge from solving a Haeckel Sphere comes from the standpoint of color symmetry. Stewart Coffin's published literature on the topic of the Jupiter puzzle seems to steer readers toward a particular coloring scheme where the 60 sticks (of wood) are divided into 6 groups of 10 each, and arranged so that every parallel stick is of the same color, as seen in this example image of the "preferred configuration". There are 4 other solutions to Coffin's classic 6-color version of the puzzle which also have color symmetry, yet do not have parallel sticks matching. Finding all 5 solutions is a fun challenge, and it could be said that the puzzle is not truly "solved" until all 5 solutions have been found. One of the satisfying aspects of solving each color symmetry challenge is that the puzzle itself takes on a whole new aesthetic with each new configuration, and sometimes the most pleasing of the five options is not necessarily the "preferred configuration" which I would define as the one which is easiest to visualize ahead of time due to having like colors touching as much as possible.

6-color cubic symmetry

One of the really interesting things about the geometry of this Haeckel Sphere is that the underlying triacontahedral structure has its own icosahedral and dodecahedral symmetry, as well as several ways to get cubic and tetrahedral symmetry. All of these different versions take advantage of different of those geometric symmetry systems in order to define the color symmetry, so for example there are three different versions of the 6-color Haeckel Sphere. The classic version, as show above in a rainbow colors, has symmetry based on the dodecahedron, whereas this earth-tone version to the left has symmetry based on the cube.



It's somewhat tricky to objectively rank all of the variations from easiest to hardest, so instead I've picked out two groups of four which I think represent a nice selection of my favorites. Scroll down to the bottom of the page to see more details about Haeckel Sphere Set #1 and Haeckel Sphere Set #2.