<｜begin▁of▁sentence｜>### Instruction:
Imagine you’re working to fill a position at a company that specializes in creating educational board games around the concept of graph theory. Your current project involves the production of a game focused on teaching players about planar graphs. The new game will feature a set of cards, each with an illustration of a graph on it. One such card is under review, featuring the graph with connections as follows: connections between points 0 and 1, 0 and 2, 1 and 2, 1 and 3, 3 and 4, 4 and 5, and finally between 5 and 3.

The design team has hit a snag though. They need to ensure that the graph depicted can be drawn in a two-dimensional plane without any of the connecting lines crossing, which is a requirement for the graph to be classified as planar – an essential concept for the educational aspect of the game. 

They've reached out to you to help determine if the illustrated graph can indeed be represented in such a manner. If it can, they require a visual planar representation to assist the artist in redesigning the card. However, if the graph turns out to not be planar, the team will need you to identify a specific subset of the graph's connections that prove its non-planarity, so they can adjust the design and educational content accordingly.

Could you delve into this matter and provide your expertise on whether this particular graph is planar or not, along with the appropriate visual or counterexample as necessary? This would greatly assist the design team in progressing with the game development and maintaining its educational integrity.
### Response:
import networkx as nx

# Create a graph
G = nx.Graph()
G.add_edges_from([(0, 1), (0, 2), (1, 2), (1, 3), (3, 4), (4, 5), (5, 3)])

# Check if the graph is planar
test_planarity, embedding_or_counterexample = nx.check_planarity(G, counterexample=True)

print('Is the graph planar?', test_planarity)
if test_planarity:
    print('Planar embedding:', embedding_or_counterexample.get_data())
else:
    print('Counterexample subgraph:', embedding_or_counterexample.edges())
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