Hi Robin , I wondered this more than 20 years ago after I finished my first telescope , a 10 inch f/10 newtonion witha 3/4 inch secondary and 3 vains , I seen the 6 spikes as well , and back then there was no internet , so I read lots of books.
The reason for 6 splkes from 3 vains is as you know the light path is crossed over at the focal plain ( thats why views are up side down)
but the 3 vains dont quite come to the same focus so they are op side down and doubled . Its a law of physics eg The wave of light .Like throwing 2 rocks into a pond and watching the waves .
I now have a curved 2 vain spider in my 10 inch f/10 and with the 3/4 inch secondary the 2 vain dont become 4 spikes .
They cancel each out , the wave theory of light . and it works, like a 10 inch refractor on the planets .
Whew ! .
Brian.