Geometric Fullerenes: Pentagon Web Rendering

🚀 Geometric Fullerenes: Pentagon Web Rendering

In this post, we explore the geometry of Fullerenes using JavaScript. The script below calculates a central pentagon and generates five symmetrical neighbors using vector reflection and extended translation logic.

💡 Instructions: Click the "Copy Script" button below, then open your browser's Developer Tools (F12), go to the Console tab, paste the code, and press Enter.

fullerene_generator.js

(function renderPerfectPentagonFlower() { const centerX = 300, centerY = 300, radius = 60; const pentagonSystem = []; // 1. Create Central Pentagon (Row 0) const row0 = Array.from({ length: 5 }, (_, i) => { const angle = (i * 2 * Math.PI / 5) - (Math.PI / 2); return { x: centerX + radius * Math.cos(angle), y: centerY + radius * Math.sin(angle) }; }); pentagonSystem.push(row0); // 2. Calculate the "Standard Side Distance" (A0 to A1) const sideDist = Math.sqrt( Math.pow(row0[1].x - row0[0].x, 2) + Math.pow(row0[1].y - row0[0].y, 2) ); // 3. Reflection Function const reflectPoint = (p, a, b) => { const dx = b.x - a.x, dy = b.y - a.y; const d2 = dx * dx + dy * dy; const t = ((p.x - a.x) * dx + (p.y - a.y) * dy) / d2; const rx = a.x + t * dx, ry = a.y + t * dy; return { x: 2 * rx - p.x, y: 2 * ry - p.y }; }; // 4. Loop to create 5 Neighbors for (let i = 0; i < 5; i++) { const vIdx1 = i; const vIdx2 = (i + 2) % 5; // Create the raw mirrored version const mirrored = row0.map(p => reflectPoint(p, row0[vIdx1], row0[vIdx2])); // CALCULATE THE EXTENDED VECTOR FOR THIS SPECIFIC SIDE // We use the "middle" point of the mirror (the one not on the axis) // To keep it consistent with your B1->A1 logic: const targetIdx = (i + 1) % 5; // The vertex between the two axis points const vSnapX = row0[targetIdx].x - mirrored[targetIdx].x; const vSnapY = row0[targetIdx].y - mirrored[targetIdx].y; const snapDist = Math.sqrt(vSnapX**2 + vSnapY**2); // Normalize and scale by (snapDist + sideDist) const unitX = vSnapX / snapDist; const unitY = vSnapY / snapDist; const totalShiftX = unitX * (snapDist + sideDist); const totalShiftY = unitY * (snapDist + sideDist); const rowExtended = mirrored.map(p => ({ x: p.x + totalShiftX, y: p.y + totalShiftY })); pentagonSystem.push(rowExtended); } // --- DRAWING --- const iframe = document.body.appendChild(document.createElement('iframe')); Object.assign(iframe.style, { width: '600px', height: '600px', position: 'fixed', top: '10px', right: '10px', zIndex: '10000', background: '#fff', border: '2px solid #000' }); const ctx = iframe.contentDocument.body.appendChild(iframe.contentDocument.createElement('canvas')).getContext('2d'); ctx.canvas.width = 600; ctx.canvas.height = 600; const colors = ['blue', 'magenta', 'red', 'orange', 'green', 'purple']; pentagonSystem.forEach((shape, sIdx) => { ctx.beginPath(); ctx.strokeStyle = colors[sIdx]; ctx.lineWidth = sIdx === 0 ? 3 : 2; ctx.moveTo(shape[0].x, shape[0].y); shape.forEach(p => ctx.lineTo(p.x, p.y)); ctx.closePath(); ctx.stroke(); // Draw dots shape.forEach(p => { ctx.fillStyle = colors[sIdx]; ctx.beginPath(); ctx.arc(p.x, p.y, 2, 0, 7); ctx.fill(); }); }); })();

(function renderPentagonWeb() {
  const centerX = 300, centerY = 300, radius = 60;
  const pentagonSystem = [];
  
  // Logic for Central Pentagon, Reflection, 
  // and Extended Translation...
  // [Click Copy to see full script]
})();

Generated with Gemini AI Tools.