Low Poly Spheres: Rhombic Triacontahedron

Low Poly Spheres: Low-poly, high-fun!

Low Poly Spheres is a series of 3D printable models of polyhedra that look like low-poly spheres. You may remember from math class that polyhedra are solid 3D shapes with flat polygonal faces, straight edges, and sharp corners or vertices. Low Poly Spheres are fun to make and display. You can print them in different colors and sizes, and use them as decorations, toys, or educational tools. Low Poly Spheres are a fun way to enjoy 3D printing and mathematics. They are simple, yet beautiful and fascinating. 

Fun Facts About the Rhombic Triacontahedron

• Geometry
  • Faces: The Rhombic Triacontahedron has 30 congruent rhombic faces.
  • Edges: It boasts 60 edges, all of equal length.
  • Vertices: It features 32 vertices.
  • Identical Faces: All faces are congruent rhombi, identical in shape and size.
  • Edge Lengths: Each face has edges of equal length, contributing to the uniformity of the polyhedron.
• Vertex Configurations
  • Two Types of Vertices:
    • 12 Vertices where five faces meet correspond to the vertices of an icosahedron. Each vertex is the meeting point of five rhombic faces.
    • 20 Vertices where three faces meet correspond to the vertices of a dodecahedron. Each vertex is where three rhombic faces come together.
• Dual Polyhedron Relationship
  • Catalan Solid: It is one of the 13 Catalan solids, which are the duals of the Archimedean solids. Specifically, it is the dual of the Icosidodecahedron.
  • Geometric Connection: In dual polyhedra, the vertices of one correspond to the faces of the other.
• Symmetry
  • Exhibits icosahedral symmetry (Iₕ), meaning it is symmetrical about the axes of both an icosahedron and a dodecahedron.
• Golden Ratio (φ ≈ 1.61803): The ratio of the long diagonal to the short diagonal of each rhombic face equals the Golden Ratio.