Low Poly Spheres: Triakis Octahedron

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 Triakis Octahedron

• Intricate Geometry: The Triakis Octahedron has 24 triangular faces, 14 vertices, and 36 edges. It is formed by augmenting each face of a regular octahedron with a pyramid, resulting in a total of 8×3=24 faces.
• Dual Polyhedron Geometric Relationship: It is the dual of the truncated cube, one of the thirteen renowned Archimedean solids celebrated for their uniform faces and vertices. In geometry, dual polyhedra have a special relationship where the vertices of one correspond to the faces of the other. This highlights the deep connections within geometric structures.
• Cubic Symmetry: The Triakis Octahedron possesses a high degree of cubic (octahedral) symmetry, making it aesthetically pleasing from all angles.
• Uniform Face Transitivity
  • Identical Faces: All its faces are congruent isosceles triangles.
  • Face-Transitive: The polyhedron is face-transitive, meaning any face can be mapped onto another through symmetry operations. This uniformity showcases the elegance of geometric principles.
• Tessellation Ability: The Triakis Octahedron can be combined with cubes to tessellate space without gaps. This property is useful in studying three-dimensional tessellations and crystal structures, where efficient space utilization is key.