# 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)