# Tiling with pentagons

Author:
mathafou
Tiling the plane with irregular pentagons - case 11 This case is defined by the conditions : A = pi/2, C + E = pi, 2B + C = 2pi, CD = DE = 2AE + BC angle D may be freely chosen between about 112° and 130° by dragging the cursor.
from the angle relations results : E = 2pi - 2D C = 2D - pi B = 3pi/2 - D Construction : Construct points C, D, E with chosen angle D and CD = DE = unit length From the above angle relations, draw line (EA) and (BC) Then to be constructed points A and B on these lines. Draw a line with angle 60° from (EA) it intersects line (BC) in I and (BC) intersects the perpendicular to (AE) from E in J on line (BC) construct points M and N with IM = IJ + IE IN = IC + IE - CD the parallel to (ME) through N intersects (EI) in P perpendicular to (AE) in P intersects line (AE) in point A, and line (BC) in point B Calculations : The sides are calculated with (CD = DE = 1) AE = CD(cos(2D) - 2cos(D))/(1 - 2cos(D)) BC = CD - 2AE AB = CD(sin(D) - 2sin(D)) - BC sin(D)