Platypus Model 1 and Model 10 pens have a shared distinctively elegant and simple shape. This blog post describes the shapes of those pen models and explains why they were chosen.
The body and cap of both models have outlines that are formed almost entirely on the intersection between two circles. They consist of a symmetrical pair of arcs truncated at the top and bottom (see the diagram below). Once that form was chosen the technical design is based on the diameters of the circles, how far apart the circles lie, and where the arcs start and end relative to the centre-line of the circles.
Apart from looking good, the smoothly curved shape of the body allows the cap to be posted relatively deeply and securely. The end of the body is naturally narrower than the inside of the cap and the smooth taper fits well within the tapered bore of the cap liner.
The cap liner obviously has to be tapered to fit inside the outer shell of the cap, but its taper is straight and slightly narrower than necessary simply to fit within the cap. Its shape is deliberately arranged such that while you are capping the pen the cap threads become aligned with the body threads before they engage. That eliminates the possibility of cross-threading, which could damage the threads in the softer cap liner material.
The cap liner also has a small step inwards about half way up. That step acts as a stopper for the widest part of the bulge at the end of the grip, and effectively seals the nib into a small volume to minimise nib drying.
The grip section of the pen has a straight taper for comfort and to give the writer plenty of options as to how to hold the pen. For the Model 1 pens the grip ends with a bulge and then a narrow portion right at the base of the nib. The bulge is what seals inside the cap, and it is set back from the nib so that the writer’s fingers are comfortably held back from the relatively short nib. The nib of the Model 10 pens is longer and so it is not desirable to move the user’s grip so far back from the nib, and thus the Model 10 grip ends very conventionally with a slight flare. Of course, that flare is what engages with the sealing step within the cap.
There is only a very slight step between the threads and the patterned body and the step is smoothly tapered. That means that the pen can be held far from the nib, if desired, without the threads and step being very noticeable. The body’s coloured band is placed between the threads and the step in order that it is neatly covered by the cap band when the cap is in place.
The cap band of Platypus pens are quite wide compared to the standard steel bands on most fountain pens. They might remind you of the wide bands on some classic models of Sheaffer pens, but the wide band is not entirely aesthetic for the Platypus pens. The inside diameter of the plain band is larger than the inside diameter of the patterned wall of the cap because the pattern thickens the wall, and because the outer diameter of the band extends just a little beyond the patterned wall. That extra diameter allows space for the cap threads and therefore minimises the extent to which the cap has to be wider than the pen body. That improves the look of the pen overall, in my opinion.
All in all, the shape of Platypus fountain pens is determined by a mixture of functional considerations and aesthetics. I like how they look and I hope that you do too.