<｜begin▁of▁sentence｜>### Instruction:
In the realm of geographical data analysis, let's consider a theoretical model where we aim to represent a small network of regions via a triadic relationship. This can be abstracted into a triangular graph structure with interconnected nodes that mirror regions or points of interest. These connections are as follows: region 0 is connected to region 1, region 1 to region 2, and region 2 back to region 0, forming a complete loop.

As a Remote Sensing Scientist, you might be engaged in the task of mapping such a network onto a two-dimensional plane for the purpose of analyzing spatial configurations in an ecological study. In this context, could you draft a proposal to simulate this network using the NetworkX library to ensure that the resulting graph can be embedded onto a plane without any of the edges intersecting inappropriately, thus maintaining the true-to-life representation of our regions? Additionally, your proposal should detail the methods utilized to confirm that the graph's placement adheres to the principles of planar embedding.

Please consider this request as a simplification of a larger remote sensing project where the integrity of spatial representations is crucial for accurate environmental mapping and analysis.
### Response:
import networkx as nx
from networkx.algorithms import planarity

# Create a graph
G = nx.Graph()
G.add_edges_from([(0, 1), (1, 2), (2, 0)])

# Initialize planar embedding
e = planarity.PlanarEmbedding()

# Add nodes in a planar embedding
for node in G.nodes():
    e.add_node(node)

# Add half edges in counterclockwise orientation
e.add_half_edge_ccw(0, 1, 2)
e.add_half_edge_ccw(1, 2, 0)
e.add_half_edge_ccw(2, 0, 1)

# Check if the structure is a valid planar embedding
e.is_valid()
print('Is the planar embedding valid?', e.is_valid())
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