In classical domain theory, single-domain (SD) grains change their magnetization by coherent rotation, where the energy barrier to domain reversal is provided by the magnetocrystalline anisotropy or by shape anisotropy for elongated grains. However, numerical micromagnetic models have shown that domain structure in SD grains is rarely perfectly uniform. For example, magnetite has significant "flowering" of its magnetization even in grains that approach the room temperature superparamagnetic (SP) size of ~30 nm. The flowering deforms slightly to accommodate the grain shape and thereby produces anisotropy independent of magnetocrystalline effects but dependent on magnetization direction within the grain. This can be similar in magnitude to that of magnetocrystalline anisotropy, even for equidimensional grains (where distance from the centroid to the grain faces is equal). The interaction of the domain structure and grain geometry is termed configurational anisotropy and has been studied mainly in relation to man-made isotropic magnetic media but received little attention in rock magnetism. In this paper we examine configurational anisotropy in SD to pseudo-single-domain (PSD) grains of magnetite using a three-dimensional finite element/boundary integral (FEBI) micromagnetic model. Equidimensional grains of magnetite of three different shapes are considered: a cube, an octahedron, and a regular tetrahedron, and in each case the effects magnetocrystalline anisotropy were removed in order to isolate the configurational anisotropy. The numerical models predict that very large coercivities are possible even for SD equidimensional grains. For tetrahedral grains coercivities of ~120 mT were obtained, which otherwise would require a grain elongation of ~1:1.75. Depending on the orientation of the principle crystalline axis to the grain shape, the configurational anisotropy may increase or decrease the overall energy barrier to domain reversal.