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#!/usr/bin/env python3
"""
Quick optimization of 7-vertex ideal polyhedron.
"""
import numpy as np
import torch
from ideal_poly_volume_toolkit.geometry import (
delaunay_triangulation_indices,
triangle_volume_from_points_torch,
)
from scipy.optimize import differential_evolution
def compute_volume(params):
"""Compute volume from spherical parameters."""
# Fixed vertices
Z = [complex(0, 0), complex(1, 0)]
# Add 4 parameterized vertices
for i in range(4):
theta = params[2*i]
phi = params[2*i + 1]
z = np.tan(theta/2) * np.exp(1j * phi)
Z.append(z)
Z_np = np.array(Z, dtype=np.complex128)
try:
idx = delaunay_triangulation_indices(Z_np)
Z_torch = torch.tensor(Z_np, dtype=torch.complex128)
total = 0
for (i, j, k) in idx:
vol = triangle_volume_from_points_torch(Z_torch[i], Z_torch[j], Z_torch[k], series_terms=96)
total += vol.item()
return -total # Negative for minimization
except:
return 1000.0 # Penalty
# Run quick optimization
print("Quick 7-vertex optimization (5 trials)...")
best_volume = 0
best_config = None
for trial in range(5):
print(f"\nTrial {trial+1}/5...")
bounds = [(0.1, np.pi-0.1), (0, 2*np.pi)] * 4
result = differential_evolution(
compute_volume,
bounds,
maxiter=100, # Reduced iterations
popsize=15, # Smaller population
seed=trial * 42
)
volume = -result.fun
print(f" Volume: {volume:.6f}")
if volume > best_volume:
best_volume = volume
best_config = result.x
# Analyze best configuration
print(f"\nBest volume: {best_volume:.6f}")
# Reconstruct for analysis
Z = [complex(0, 0), complex(1, 0)]
for i in range(4):
theta = best_config[2*i]
phi = best_config[2*i + 1]
z = np.tan(theta/2) * np.exp(1j * phi)
Z.append(z)
Z_np = np.array(Z, dtype=np.complex128)
idx = delaunay_triangulation_indices(Z_np)
# Count faces and vertices
vertices_used = set()
for (i, j, k) in idx:
vertices_used.update([i, j, k])
print(f"\nCombinatorial structure:")
print(f" Vertices used: {len(vertices_used)}")
print(f" Triangular faces: {len(idx)}")
# Check vertex degrees
degrees = [0] * 7
for (i, j, k) in idx:
degrees[i] += 1
degrees[j] += 1
degrees[k] += 1
print(f" Face counts per vertex: {degrees}")
# Classification
if len(vertices_used) == 6 and len(idx) == 8:
print(" → Looks like an octahedron")
elif len(vertices_used) == 7 and len(idx) == 10:
print(" → Looks like a pentagonal bipyramid")
elif len(vertices_used) == 7:
print(f" → 7-vertex polyhedron with {len(idx)} faces")
print(f"\nRegular octahedron volume: ≈ 5.333")
print(f"Ratio: {best_volume/5.333:.3f}") |