Deltoidal Hexecontahedron

Sixty identical kites dance around a sphere to make this stunning Deltoidal Hexecontahedron.

Style: This polyhedral design is part of the Catalan Wireframe series, with an organic and soft feel that distinguishes vertices of different degrees. Each of the thirteen polyhedra in the series are scaled so that they have similar edge-to-surface area ratios, so they look great in groups or as a full set.

Looking for a birthday or anniverary gift? A Deltoidal Hexecontahedron makes a nice keepsake gift to mark occasions that involve the following numerical milestones:

• 3 = number of vertex types
• 3, 4, 5 = number of edges coming into each type of vertex
• 12 = number of vertices of degree 5
• 20 = number of vertices of degree 3
• 30 = number of vertices of degree 4
• 60 = total number of faces
• 62 = total number of vertices
• 120 = total number of edges (maybe it's your 120-day anniversary?)

 

Want to wear it? This model is also available in a version that includes a loop, so that you can wear it as an earring or necklace pendant.

Want it fancier? You can also buy this model in high-end materials like cast Sterling Silver or plated Gold. 

Want a companion piece? You can also order a model of the dual of this polyhedron. Or take your pick from all thirteen Catalan wireframes or all thirteen Archimedean wireframes.

Mathematics: The Deltoidal Hexecontahedron is one of the thirteen Catalan solids. "Deltoidal" means "kite-shaped" and "hexeconta" means "sixty," indicating that this polyhedron has 60 kite-shaped faces.  The Deltoidal Hexecontahedron has 60 identical four-sided faces and three types of vertices, of degrees three, four, and five. Its dual polyhedron, the Rhombicosidodecahedron, turns things inside-out with 60 identical degree-four vertices and three types of regular polygon faces, with three, four, and five sides. 

Design: This model was created by mathgrrl using Mathematica, Meshmixer, MeshLab, and TopMod. Read more at Stylized Catalan Wireframes on MakerHome, or download desktop-printable early versions of these models at Catalan Wireframe Polyhedra on Thingiverse. 

Photo Discount: Earn $5 of Shapeways credit from me by ordering and photographing this design in a new material! If you're the first to send me a well-staged, good quality photo of this design in a material for which this listing does not yet have a real-world photograph, then I'll send you $5 credit that you can spend anywhere on Shapeways.