Continuing to explore the potential for icosahedral single-sheet polyhedra, this model manipulates the proportions of Semi-Sunken Icosahedron and uses a grid of alternating hexagons and triangles to achieve a shape like a soccer ball.

After the success of the Stellated Icosahedron Starball, I explored a number of other single-sheet polyhedral models using the icosahedron as a base. The Semi-Sunken Icosahedron seems to arrive at the essence of the series, as it can be folded from a basic 12x12 triangular grid on a hexagonal sheet. The finished object is fascinating to look at, revealing an octahedral geometry at the level of individual faces. In addition, the model is easier to fold and lock is very strong.

The original inspiration for this model was taking a fresh look at one of the forms I was trying to create in my Starball explorations. The key idea was twelve star shapes embedded on a single-sheet polyhedron the resembles a ball or sphere. Early attempts were from a dodecahedron base, using pentagonal symmetry on the folded sheet, but this proved to be very complicated and the stars did not have enough depth to really pop. I was on the plane to CFC3 in Bogota, Colombia, when I reimagined the subject using an icosahedron as a base. Mathematically the model is a stellated icosahedron, but the sunken inner flaps are allowed to open up a little to reveal the star-shaped areas. In addition to capturing the look I was going for, it is much easer to fold than its predecessor, as it develops from a triangular grid on a hexagonal sheet of paper.