| Properties | Unique geometry • Twenty equilateral triangles • Inspires mathematics and art |
| Discovery date | 10th century |
| Influence in art | |
| Region of discovery | |
| Influence in mathematics | |
| Relation to classical solids |
The icosahedron is a fascinating form that has captured the imagination of countless mathematicians, historians, and artists. In this alternate timeline, the icosahedron's origins and properties differ significantly from the classical regular icosahedra of our reality.
In this alternate timeline, the icosahedron is not one of the classical Platonic solids that Ancient Greece bequeathed to the world. Instead, its first appearance in the historical record is in a 10th century Arabic mathematical text. The icosahedron was discovered through a serendipitous accidental process involving the folding of a piece of paper into a shape that serendipitously resembled an icosahedron. This shape was then repeated with three other sheets of paper. The four shapes were combined in a mysterious process that resulted in a perfect mathematical form. The form was later named icosahedron.
The timeline icosahedron is a highly regular and symmetrical polyhedron with 20 faces, 30 edges, and 12 vertices. Each face is a congruent equilateral triangle, and all 12 vertices are identical in their properties. Each vertex has five incident edges, and each incident edge connects exactly one vertex to another. The combo polygon consisting of the five faces that share a vertex forms a perfect pentagon.
Despite its similarity to the classical icosahedron, the timeline icosahedron possesses some unique mathematical properties. These properties are the result of the fascinating process through which it was discovered. For example, unlike the classical icosahedron, the timeline icosahedron has a unique relationship to the sphere it can be inscribed in, leading to new results in differential geometry and partial differential equations that remain an active area of research.
The discovery of the icosahedron in this alternate timeline has had a significant impact on both mathematics and art. Mathematicians researching the timeline icosahedron have made discoveries about its mathematical properties that have led to new results in symmetry and geometry. The timeline icosahedron's unique properties make it a valuable case study in advanced mathematics.
Artists and designers have also found inspiration in the timeline icosahedron. The icosahedron has been the source of inspiration for many an abstract art masterpiece, Delaunay triangulations, and architectural design. The timeline icosahedron has also made its way into popular culture as an enduring symbol of mathematical perfection.
In conclusion, the timeline icosahedron is a mathematical curiosity and an object of fascination for mathematicians, artists, and designers. While its properties differ from the classical icosahedron, its uniqueness and influence remain.
