Low Poly Spheres: Tetrakis Hexahedron

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 Tetrakis Hexahedron

• Complex Structure: The Tetrakis Hexahedron has 24 triangular faces, 14 vertices, and 36 edges. Each of the six faces of the original cube is replaced with a pyramid composed of four new triangular faces, totaling 6×4=24 faces.
• Dual Polyhedron: It is the dual of the truncated octahedron, which is one of the thirteen Archimedean solids known for their uniformity and symmetry.
• Symmetry: The Tetrakis Hexahedron possesses a high degree of octahedral symmetry, making it aesthetically pleasing from all angles.
• Uniform Face Transitivity: All its faces are congruent isosceles triangles, and the polyhedron is face-transitive, meaning any face can be mapped onto another through symmetry operations.
• Space-Filling Property: The Tetrakis Hexahedron can be combined with octahedra to tessellate space without gaps, making it useful in studying three-dimensional tessellations and crystal structures.
• Applications: This shape finds relevance in fields like crystallography, geometry, and architecture due to its unique properties and visual appeal. It's observed in natural crystal formations and is used to model complex structures.