A hexagonal greenhouse is a structure with six sides joined so as to enclose a hexagonal space, topped with a roof made of six triangular panels that all meet at the centre. The frame is usually made of wood or aluminium, and the triangular panels are generally made of toughened glass or polycarbonate. There are no particular advantages to the shape; it is a matter of taste.
Sides - Frames
The angles of the joints of the frames of the six sides are all 90 degree angles. This is because the frames are rectangular.
Sides - Panels
For a hexagonal greenhouse, the angles of the joints of the panels -- the sections within the frames -- of the six sides are all 90-degree angles as is true of traditional rectangular greenhouses. Different angles can be used for a non-traditional look. The structural integrity of the greenhouse will not be compromised so long as you do not damage the frames of the six sides.
The angle of cut of the three members of each of the six roof trusses is 120 degrees. Each set of three will then fit together to make a triangular frame for each roof panel.
Roof - Triangular Panels
Cutting angles on glass is a specialised job. The job is far easier with polycarbonate. As do-it-yourself experts Albert Jackson and David Day point out, cutting glass is not usually necessary as suppliers will do it for you. The general principles, however, are the same. The angles vary according to the pitch, or the angle of the slope of the roof, and must be worked out with simple geometry depending on the dimensions of the greenhouse. If you live in an area that experiences high levels of snowfall, follow Ortho's advice and have a higher pitch as this prevents ice and snow build-up. This will mean the base angles of the six triangles will be greater than 60 degrees and the top angles will be less than 60 degrees.