Simple 2 D plane polygonial cyclic configurations ( below 7 edges ) :
hexagram - A Hexagram is composed from two of the eight trigrams. Its bars are encoded as binary numbers, from bottom to top, using the digits from left to right.
/ water and snow structures, coin tosses, permutations, the most common in nature, ... /
pentagram - A pentagram is a polygon that looks like a 5-pointed star. The outer vertices (points of the stars) form a regular pentagon.
/ apple structure, combinatorics, flower petals, starfish, ... /
square - four-sided regular polygon which is also known as a quadrilateral with four equal sides.
/ square box jelly, many different species of plankton, and even each and every plant cell, ... /
triangle - polygon with three edges and three vertices. In traditional texts it is said that the trigrams are doubled to form a hexagram.
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# draw nodes and edges, regular pentagram in regular pentagram using plotly
import networkx as nx
import matplotlib.pyplot as plt
import numpy as np
G = nx.petersen_graph()
# set 2D edge positions
import math
pos2d = {}
for i in range(5):
theta = 2 * math.pi * i / 5 + math.pi / 2
pos2d[i] = (2 * math.cos(theta), 2 * math.sin(theta)) # outer vertices
pos2d[5 + i] = (math.cos(theta), math.sin(theta)) # inner vertices
for v in G:
print('%d: (%6s, %6s)' % (v, '%.3f' % pos2d[v][0], '%.3f' % pos2d[v][1]))
vis = GraphVisualization(G, pos2d)
fig = vis.create_figure()
fig.show()
Refrences:
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