Low Poly Spheres: Deltoidal Icositetrahedron

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 Deltoidal Icositetrahedron

• Intricate Geometry : The Deltoidal Icositetrahedron has 24 faces, 48 edges, and 26 vertices. Each face is a congruent kite-shaped quadrilateral (also known as a deltoid), giving it a distinctive appearance.
• Dual Polyhedron Relationship: It is one of the 13 Catalan solids, which are the duals of the 13 Archimedean solids. It is the dual of the rhombicuboctahedron. In dual polyhedra, the vertices of one correspond to the faces of the other, showcasing a deep geometric connection.
• Octahedral Symmetry:  The polyhedron possesses octahedral symmetry (symmetry group Oh), meaning it is symmetrical about the axes of an octahedron. This high degree of symmetry makes it aesthetically pleasing from all angles.
• Uniform Face Transitivity: 
  • Identical Faces: All faces are congruent kites, identical in shape and size.
  • Face-Transitive: Any face can be mapped onto another through symmetry operations, highlighting its uniform geometric structure.
• Edge Varieties: The Deltoidal Icositetrahedron has two types of edges:
  • 24 shorter edges where two shorter sides of kites meet.
  • 24 longer edges where two longer sides of kites meet.
• Vertex Configurations: There are three types of vertices:
  • 8 vertices where three edges meet (two short and one long edge), corresponding to the vertices of a cube.
  • 12 vertices where four edges meet (two short and two long edges), located along the edges of the cube and octahedron.
  • 6 vertices where eight edges meet (all long edges), corresponding to the centers of the faces of an octahedron.