This coral-inspired model (with 3-fold rotational symmetry) was generated with a single mathematical expression using the implicit surfaces filter in MeshLab. Please check out all of the other implicit surfaces at vertigo polka.
Here is a silver bauble made from two nested icosahedrons, connected to each other at the center of each of their twenty triangular faces. Check out my other pendant models in my Jewelry/Pendant section.
This silver bauble started out as two octahedrons of different sizes. The faces have been separated and rotated so that the vertices of each of the smaller triangles touch a vertex of one of the larger triangles.
This model is made of a two continuous bands that wrap diagonally around a torus shape 45 times before connecting to the original starting points. Here's two more Spiral Tori: Spiral Torus 110mm and a colored version Holiday Spiral Torus
This part consists of all five Platonic Solids nested one inside another.
From largest to smallest, there is an icosahedron (20 triangular faces), a dodecahedron (12 pentagonal faces), a hexahedron (6 square faces), a tetrahedron (4 triangular faces) and an octahedron (8 triangular faces).
The overall shape is a Rhombic Triacontrahedron, a combination of an icosahedron and dodecahedron). These can be nested infinitely following the same order.