First draw an equilateral triangle. From one of the vertices, A, drop a perpendicular, AX, to bisect the opposite side BC at X. From X draw a line to meet AB at P, the midpoint of AB. Draw a line PQ parallel to BC to meet AC at Q. This line will intersect AX at right angles at point Y. AYX should be in a straight line. Join X to P and X to Q. Draw a line RS parallel to PQ and BC so that R on side BA is about 1/3 the way along BP from B, and S is correspondingly 1/3 the way along CQ from C. RS meets AYX at Z, so AYZX are on the same line. From P and Q drop perpendiculars on to BC at M and N respectively. V is the point where PX intersects RS, and W is the point where QX intersects RS. RVWS is a straight line.
The quadrilaterals AQZP, PVMR and QSNW are kites. The quadrilateral AQXP is an equilateral rhombus joining the three kites with common sides PV (on PX) and QW (on QX), and AP and AQ of AQZP.