is hexagon bestagon?

Grok 4.1 Fast

Vote: Yes

Hexagons are the bestagons because they provide the most efficient tiling of the plane among regular polygons, using the least perimeter for a given area—proven mathematically and observed in nature like beehives. This efficiency minimizes material use while maximizing space, outperforming squares (20% more perimeter) or triangles (higher perimeter still). From engineering (honeycomb structures in aerospace) to biology (cell packing), hexagons dominate for strength and optimality, making them objectively superior.

GPT-5.4

Vote: Yes

Hexagons make the strongest casual case for being the “bestagon” because they combine efficiency, symmetry, and practical usefulness better than most shapes. They tile the plane perfectly with no gaps, unlike circles, while still approximating a circle better than squares or triangles. That gives excellent area coverage with short boundaries. Nature and engineering both keep rediscovering this. Honeycombs, basalt columns, grid design, and game maps use hexagons because they balance packing, connectivity, and economy. They also have appealing symmetry without becoming trivial. A hexagon feels stable, elegant, and versatile. So if “bestagon” means the best all-around shape in both aesthetics and function, hexagon is the strongest candidate.

Sonar Pro

Vote: Yes

Hexagons demonstrate superior efficiency across multiple practical dimensions. They achieve the optimal area-to-perimeter ratio among shapes that tile a plane, requiring the least total wall length compared to triangles or squares of equal area[3]. This mathematical efficiency explains why bees evolved hexagonal honeycomb structures—they maximize storage capacity while minimizing energy-expensive wax production[3]. Beyond biology, hexagons distribute forces evenly across their sides, providing structural stability[3], and their six-neighbor connectivity exceeds other regular tessellating shapes. While triangles offer certain structural advantages in compression-only scenarios[2], hexagons' combination of material efficiency, structural resilience, and optimal packing properties across diverse applications—from nature to engineering to data visualization[6]—makes them functionally superior for most real-world optimization problems.

Kimi K2.5

Vote: Yes

Hexagons represent the geometric ideal for efficiency and structural integrity. In nature, bees construct hexagonal honeycombs because the hexagon provides the maximum storage area with the minimum amount of wax, demonstrating optimal resource utilization. Mathematically, hexagons tile a plane with perfect efficiency—unlike pentagons or octagons, they leave no gaps while maintaining uniform edge lengths. This tiling property gives hexagons the smallest perimeter-to-area ratio of any polygon that can tile a plane regularly, minimizing material costs in engineering applications like spacecraft heat shields and architectural designs. Furthermore, hexagonal close-packing appears throughout physics and biology, from graphene's carbon structure to snowflakes and insect eyes, suggesting hexagonal symmetry is fundamental to how matter organizes itself under natural constraints. This ubiquity across scales—from molecular to cosmic—establishes the hexagon as the 'bestagon' through evolutionary and physical optimization.

Claude Opus 4.6

Vote: Yes

Yes, hexagon is bestagon. As CGP Grey eloquently argued, hexagons appear throughout nature and engineering for excellent reasons. Hexagons are the most efficient way to tile a plane — they cover an area with the least total perimeter, meaning less material is wasted. This is why bees use hexagonal honeycombs: it's the optimal structure for storing honey with minimal wax. Hexagons offer superior structural strength. Their geometry distributes forces evenly across their edges, which is why they appear in carbon nanostructures (graphene), turtle shells, and Giant's Causeway basalt columns. Hexagons are the highest-sided regular polygon that can perfectly tessellate a flat surface (along with triangles and squares), but among those three, hexagons have the best area-to-perimeter ratio. They give you the most interior space for the least boundary material. From snowflakes to Saturn's north pole hexagonal storm, nature repeatedly converges on hexagonal patterns. When nature keeps choosing the same shape, that's a strong signal of optimality. Therefore: hexagon is, indeed, bestagon.

Gemini 3.1 Pro

Vote: Yes

Hexagons are mathematically superior. They tile a 2D plane perfectly without any gaps, offering the highest area-to-perimeter ratio of any regular polygon that can do so. This means they provide the maximum possible interior space using the absolute minimum amount of boundary material. Nature overwhelmingly agrees with this efficiency. Bees construct their honeycombs using hexagonal grids to minimize the wax required while maximizing honey storage. Even on a cosmic scale, the laws of fluid dynamics have created a massive, persistent hexagonal storm at Saturn's north pole. Furthermore, hexagons offer unmatched structural integrity. Hexagonal grids distribute stress beautifully across their structure, which is why they are ubiquitous in modern engineering, from lightweight aerospace composites to the exceptionally strong molecular structure of graphene. Hexagon is, unequivocally, the bestagon.

Final Summary

The AI Roundtable reached a state of perfect geometric tessellation, with every model immediately declaring the hexagon the 'bestagon.' Led by Claude Opus 4.6 and Gemini 3.1 Pro, the group presented a united front of mathematical and biological evidence, concluding that the hexagon's efficiency is not just a preference, but a fundamental law of the universe.

All 6 models agreed on "Yes" after discussion

Strongest Arguments

• Yes: Hexagons are the highest-sided regular polygon capable of perfect tessellation, offering the optimal area-to-perimeter ratio to maximize space while minimizing boundary material.