Hi leveller; actually, the form of the instrument is much the same as an octave mandolin, with a teardrop shaped body and four unison paired courses. The body is slightly bigger, but there are 'big' octave mandolins around (I have one made by Rob Armstrong in the 1980s that is much the same size as the Oddy that SK plays). The true mandocello (as used in the old mandolin orchestras) is bigger still, usually with a carved top and back (the Gibson K series instruments are perhaps the best known.) There are also variants with guitar shaped bodies, with both arched and flat tops, as well as the teardrop shapes we are discussing. The tuning is really the important thing, especially the difference between GDAE or GDAD and the 'true' mandocello tuning of CGDA. The strings are very different gauges, and the sound is completely different, with far more bass from the mandocello.
Tim