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 hemis 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 They are approximately four inches (approx 100mm) in diameter and were originally made using coloured polyester gel coat.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 (right) 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...
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 (approx) 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.