Spiders have the important function of holding The Secondary Mirror or Flat in place.  That is simple enough, yet more demanding than it first seems. The major requirements being that good Spider will offer a minimum obstruction to incomming light, and will dampen ground vibrations transfered through the telescope's mount, and main tube. These vibrations cause the image to jitter and can be very annoying.
Today's Spiders go beyond this, supporting heated Flat Holders that keep their flats from dewing over on a cold night. Here the spider's vanes carry the electrical current to avoid messy wiring.  A 3-Vane Spider offers less obstruction to incomming light than a 4-Vane Spider does, but will resonate with ground vibrations if it is used to support a large Flat.  Four-Vane Spiders are required to dampen ground vibrations in Flats larger than 2".