Shape-adjustable heliostats can maintain a focused image of the solar disc on a receiver target throughout the day, as the angle of incidence (AOI) changes on the reflector. This requires the heliostat reflector to be deformed into a unique biconic concave shape dependent on AOI. The reflector comprises a single rectangular sheet of silvered float glass mounted to a steel frame. Its shape is set initially, by adjusting the height of mounting points, to the biconic shape required for imaging at 60 degrees AOI. Shapes for other AOIs are obtained by twisting the frame from its four corners and center. A finite element model was made of a heliostat designed to form a disc image on a 130 m distant receiver using a single sheet glass reflector, 1/8” thick x 130” x 96”, supported by 58 points on a rectangular tube frame structure weighing 120 kg. Analysis shows an overall RMS slope error <1 mrad for all AOI from 0 to 70 degrees. Without twisting, the RMS slope error would be ~3.5 mrad at 0° and 70° AOI. Preliminary results from analysis of slope error maps generated from the FE model indicate encircled energies within the ideal solar disc radius of >85% are achievable. Models of fields of closely packed heliostats of this type, on target axis mounts, demonstrate a geometrical throughput into the receiver of >73% of the total mirror area, after accounting for blocking, shadowing, and cosine loss. In one model, with 450 heliostats powering five compound parabolic concentrators at a receiver, a concentration of > 3,000 was obtained at powers > 1 MW, through much of the day.