There are fifty-six of them (forty-eight on the 2010 re-designed Dalek) and they live on the surface of the Dalek skirt. The hemispheres have been a Dalek trademark from the very beginning. They were originally blue, but were rarely seen in this colour - the episodes featuring them were made in black and white. Only the movies show us the Daleks with this colour scheme. Later hemispheres were painted black and later still, bronze and gold...
Not quite a full hemisphere, but more of a teardrop shape, the original hemispheres were made from fibreglass. They are approximately four inches (approx 100mm) in diameter and were originally made using coloured polyester gel coat.
All original 1960s 'Shawcraft' Daleks had hemispheres which were fitted inside the skirt and protruded through holes in the panels. The hemis had a flat flange that allowed them to be fixed to the interior surface of the skirt. The hemispheres on all movie Dalek skirts had an alignment feature that makes these skirts easy to spot.
In the 1970s the hemispheres were almost always painted black. The hemispheres on the original skirt sections used in the previous decade were retained. New skirt sections also began to appear and with them came new hemispheres. Some of these were no longer teardrop-shaped. Some were larger than four inches in diameter. Some were oddly spaced.
The most important change from a construction point of view was the introduction of surface-mounted hemispheres that bolted onto the outer surface of the skirt. Pictured is the Tussaud's skirt which originally had hemispheres made from ball float valves. Surprisingly, these were fitted using the traditional 'push through' method.
Imperials and Renegades...
With the introduction of the Imperial and Renegade Daleks in the 1980s, there came a slightly modified hemisphere design. The distribution became very even with extra space at the top and bottom of the skirt. The hemisphere size also reduced slightly.
These hemispheres were all attached using the 'bolt-on' method. This is evident in the aftermath of the exploding builder's yard doors, where one Dalek has had several hemispheres blown completely off the skirt, leaving only the bolt holes behind (click on the photo for a better look).
The 2005-2010 Series Dalek has hemispheres which, like the skirt, are a return to the original design from the 1960s. A welcome return of the most effective hemisphere configuration, complete with (approximately) four-inch diameter and even distribution on each panel.
The main cosmetic difference is the addition of a black bezel, made from an automotive oil seal, around each hemisphere. Later bezels were resin castings of the same type of seal. The method of hemisphere attachment remains the same as 1980s Daleks - they are surface mounted using bolts.
The huge 2010 re-designed Daleks have equally huge hemispheres. While the norm has always been around the four-inch diameter mark, (with Imperial Daleks hemispheres being even smaller), these beasts sport hemispheres, the size of which has not been seen since the ball-float days on the 1970s (see above).
The surrounds used on the earlier new series props have been deleted and the hemispheres are now attached directly into shallow recesses, in the skirt panels. This makes their alignment consistent and also gives them a faux 'push-through' look.
Resolution and Revolution...
The 2019 story Resolution features a Dalek skirt which has been manufactured by the Dalek creature as a replacement for original unit, which was destroyed. There is no reference as to what the original Reconnaissance Dalek 'travel machine' might have looked like. We have to assume that it was either vastly different from all other Daleks previously seen or that the mutant was stuck for time and materials and just threw the casing together with little regard for accuracy.
Either way, the end result is unusual. For the first time, we see a Dalek with hemispheres that vary is size (on the same prop). Some are absolutely huge, whereas the others appear to be significantly smaller in diameter than any seen before. Each hemisphere has a small, unobtrusive flange. The odd columns of three hemispheres, (rather than the traditional four) make for uncomfortable viewing.
By the time the narrative is continued, in the 2021 story Revolution Of The Daleks, the lash-up Dalek seen previously has been used as inspiration. Humans have taken the remains of the original casing and refined it, producing something more in line with what we expect a Dalek to look like.
As part of this refining process, the hemispheres have been reverted to something more like their usual size. On certain panels they still only appear in columns of three, with the remaining areas filled with raised panel detail. Each hemisphere now has a very thick and prominent aluminium/silver flange. This links the design nicely back to the original bronze New Series Daleks.
When considering the method of hemisphere production, a Dalek builder must first decide whether they are to be fitted as 'push-throughs' or as 'bolt-ons'. If a classic Dalek is being built, 'push-throughs' are a good option and can be made quite cheaply using PETG plastic sheet.
The sheet is cut up into small squares that are clamped into a frame and heated. The hot, pliable plastic is then pressed over a hemisphere-shaped mould which forces the plastic into the correct shape. The clear hemispheres can then be painted on the inside and fitted using the flange created during the pressure-forming process.
Fibreglass is also an ideal material for hemisphere production. The hemispheres can be made using a pigmented gel coat, so painting is not necessary. To make hemispheres from GRP, a mould must be made from an existing hemisphere. Dalek builders will often make a mould that enables them to cast many hemis in one go.
The inset photo shows one indentation from an eight-hemisphere mould. Fibreglass hemispheres can be either flanged for 'push-through' mounting or simply cut off for 'bolt-on' mounting. 'Bolt-on' hemispheres require additional work, securing the bolt head to the inside centre.
A quick and easy way of making hemispheres is to use commercially available plastic parts. Toy vending machine capsules and sweet canisters are ideal candidates if they can be found in sufficient quantities, at the right price.
Since they don't have a flange, they must be fitted using the 'bolt-on' method. They can be strengthened using circular off-cuts of MDF, glued to the inside.
Expanding foam and resin have also been used by many Dalek builders to add strength and provide a means of holding the central bolt in position. These hemispheres are painted on their external surface prior to fitting.