you cannot create a network with only one odd vertice because then the network would end straight away and that the network would not be complete
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Yes
Yes
true
Yes. That's always possible, but there's only one of them.
No. Each interior angle of a regular pentagon is 108 degrees. In order for tessellation to be possible, the sum of the angles meeting at a point must be 360 degrees. That is to ensure that all the space around that point is covered. But 108 is not a factor of 360 so it is not possible.