- DESIGN INFO
- Designer
- Year2024
- Description
- Notes

- PIECE INFO
- Pieces (Total):12
- Unique Shapes:1
- Solutions:5
- Apparent Solutions:
- Moves (First Piece):
- Moves (Total):
- Solution Notes:

- DIFFICULTY
- Combination:4
- Sequence:2
- Dexterity:3
- Discovery:2

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.

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.

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.

This version with an "ice cream sundae" color theme has a checkerboard of two kinds of tetrahedral symmetry, sort of like a soccer ball. Despite that all three versions that I've shown here all have 6 colors, they are each vastly different puzzle solving experiences because of the mental visualization needed in order to correctly place each piece next to its neighbors in order to get the the proper symmetry system. Another factor at play in differentiating the solving experience from one version of the Haeckel Sphere to another is the question of how many colors are involved, and whether or not there are multiple copies of identical pieces. For example the 6-color cubic Haeckel Spheres (shown above in earth-tones) has 12 different pieces whereas the 3-color Haeckel Spheres (which also have cubic symmetry) has 4 identical copies of each of the 3 pieces, and the 2-color checkered Haeckel Spheres have all 12 pieces the same, which actually makes it pretty hard to solve because the colors don't give you much of a clue about what is supposed to go where.

It's somewhat tricky for me to rank the relative difficulty of each version, however here's a starting point:

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.

6-color tetrahedral symmetry

This version with an "ice cream sundae" color theme has a checkerboard of two kinds of tetrahedral symmetry, sort of like a soccer ball. Despite that all three versions that I've shown here all have 6 colors, they are each vastly different puzzle solving experiences because of the mental visualization needed in order to correctly place each piece next to its neighbors in order to get the the proper symmetry system. Another factor at play in differentiating the solving experience from one version of the Haeckel Sphere to another is the question of how many colors are involved, and whether or not there are multiple copies of identical pieces. For example the 6-color cubic Haeckel Spheres (shown above in earth-tones) has 12 different pieces whereas the 3-color Haeckel Spheres (which also have cubic symmetry) has 4 identical copies of each of the 3 pieces, and the 2-color checkered Haeckel Spheres have all 12 pieces the same, which actually makes it pretty hard to solve because the colors don't give you much of a clue about what is supposed to go where.

It's somewhat tricky for me to rank the relative difficulty of each version, however here's a starting point:

- the solid color versions (1-color and 12-color) have no color symmetry challenges so they are the easiest
- the easiest ones which do have color symmetry are those which have color symmetry geometry matching the axis of disassembly, so that means the classic 6-color as well as the 2-color dipped versions.
- the 4-color dipped is also relatively easy, however the symmetry is off the axis of disassembly
- the versions that have lots of colors (10-color and 12-color mixed) are a little bit tricky to get started, but once you get a few pieces properly placed then it's relatively easy to figure out where the rest of the pieces go becaue the proper positions are color coded
- the versions that have fewer colors tend to be more difficult because the proper pieces positioning is not obvious (the opposite of being color coded) so for example the 2-color polar, and especially the 2-color checkered versions are challenging
- I have personally found that the versions with tetrahedral symmetry are the most challenging, such as the 5-color and 6-color checkered ones

- 10-color Haeckel Spheres
- 12-color mixed Haeckel Spheres
- 12-color solid Haeckel Spheres
- 2-color checkered Haeckel Spheres
- 2-color dipped Haeckel Spheres
- 2-color polar Haeckel Spheres
- 3-color Haeckel Spheres
- 4-color dipped Haeckel Spheres
- 4-color tetrahedral Haeckel Spheres
- 5-color Haeckel Spheres
- 6-color checkered Haeckel Spheres
- 6-color classic Haeckel Spheres
- 6-color cubic Haeckel Spheres
- solid color Haeckel Spheres

IMAGES