What type of rig is this?

I might call it a ketch, but both masts are the
same height, and both mains look to be the same
(might be nice to be able to interchange main
& mizzen).

 

I think is a ketch. The mizzen mast is in front of the rudder. A yawl on the other hand has the mizzen behind the rudder post.

I thibnk that generally the mizzen mast is shorter on both, but the difference between the two is based on the possition of the mizzen, not the size of the mizzen.

Mari Cha IV has also the same aspect...

 

I believe the designer was Chuck Burns and I believe he called it a schooner rig.

That is, if the boat in the photo is in fact Sir Isaac.

http://chuckburns0.tripod.com/sirisaac

However, it appears they have modified the rig and added a boom to the foremast. So would that now make it a ketch?

Didn't one of the configurations of the Chance designed Ondine have equal height masts, and was called a ketch? Ditto Mari Cha IV?

 

It is indeed Sir Isaac.
The race was Winter Vashon.
A stately vessel in photographs, and even moreso in person.
(I've only seen her from other boats, no idea what the accomodations
are like, but more plush than on a Synergy 1000, I'd bet).

Thanks for the link...
I followed it, and found a picture of her with two booms:
http://chuckburns0.tripod.com/sirisaac/id12.html

Apparantly also available rigged as a sloop:
http://chuckburns0.tripod.com/sirisaac/id11.html

I think with a high aspect ration deep draft keel
the sloop rig would be a fast boat with lots
of creature comforts.

 

Sir Isaac is a schooner, because the masts are the same height. If the aft mast was shorter, it would be a ketch.

Whether or not there is a boom on the foremast doesn't affect it being a schooner, but rather would make it either a regular schooner or a 'staysail' schooner, I believe.

 

I've always seen them called "French Schooners", or Schetches.