One of the 8 ways to join regular pentagons per Matt Parker’s video and described in this PDF.

This model cannot be built exactly using any of the algebraic fields supported by vZome. This model is a rational approximation accurate to 5 decimal places. The exact values used in the coordinates are determined by a series of 3 equations. The equations and their solution can be seen on Wolfram Alpha.

Four folded pentagons using net P4.1