A geometric construction system includes: a plurality of flat panels; and a plurality of connecting units provided on side edges of the flat panels. Each connecting unit includes first and second engaging parts. The first engaging part is formed with a protrusion, and the second engaging part is formed with a recess such that the protrusion of the first engaging part on one of the flat panels is releasably engageable with the recess of the second engaging part on another of the flat panels. The second engaging part is further formed with resilient claws that project from a periphery of the recess. The claws of the second engaging part on one of the flat panels clamp resiliently the protusion of the first engaging part on another of the flat panels when the protrusion is moved into the recess of the second engaging part.