This is a partial 600-cell (a 4 dimensional regular polytope, the 4D equivalent of a regular icosahedron, with tetrahedral 'faces' called cells). It's also called an icosaplex or a polyicosahedron. This is a vertex centered perspective projection of part of that shape into 3D. It includes only the central 115 tetrahedra out of the 600, in 10 strips: 5 central spine strips, and 5 more outer strips which spiral around the spine. There would be 20 of these strips in total, if the entire 600-cell were included in the puzzle. Each strip would then have 30 tetrahetrons, and the centers of each strip's tetrahedra would lie on a circle, with each strip interlinked with every other one. This is because the 600-cell vertices all lie on the 4D unit hypersphere (and their centers on a slightly smaller hypersphere), and the Hopf Fibration provides a 1-1 mapping into 3D of the decomposition of the 600-cell into 20 strips, with the centers of the tetrahedra (and also their vertices) lying on circular fibers. This puzzle was inspired by Henry Segeman's and Saul Schleimer's Quintessence puzzle, also available on Shapeways, and this puzzle is a dual of an inner part of of that puzzle, part of a 120-cell, the dual of the 600-cell. This puzzle is in the shape of a Stellated Dodecahedron (with 60 faces- please see the attached rendering). Point to opposite point, the assembled puzzle is 5.74 cenimeters in diameter (2.26"). Because the plastic is a bit flexible, the pieces will pop together and stay together.