Thanks for your message, Robert.
I don't want to pretend to be a geologist, so I suggest you contact the
Saudi Geological Survey or the US Geological Survey here in Jeddah for
expert answers to your question. They are very kind about assisting the
public. Contact Mr. Maher Idris at   mhidris@sps.net.sa    or Mr. Tim Hayes
at   thayes@usgs.gov

It looks to me like the mineral you are describing is popularly called a
Sand Rose, a very beautiful gypsum formation found under the sand in salty
areas.   Saudi Diamonds, instead, are clear pieces of quartz, somewhat
polished by the wind.
J. Pint