The skeletal morpologies of three-sided silicoflagellates can be reproduced by a mathematical model that minimizes the apical surface area. The model allows the basal sides to bow outward; the morphology that best minimizes apical area has a basal ring that approximates a circle. More typical silicoflagellates from the geologic record, however, tend to have a basal ring more triangular in outline; our modeling shows that this can occur where the reduction of skeletal material, and thus weight, is a secondary factor. A model that minimizes the use of skeletal material produces unusual morphologies, indicating that the reduction of skeletal material is not of primary importance.