Time-geographic concepts are effective tools for the geovisualization of human activity patterns and to assess individual accessibility. In their traditional form, however, time-geographic concepts assume uniform travel velocities in an isotropic and homogeneous space. Because transportation systems confine travellers to links of road and rail networks with time-varying flows, these premises are typically unsatisfied in real-world situations. This paper provides an innovative approach to ameliorate the realism and applicability of space-time prisms by developing new three-dimensional space-time objects. Three-dimensional solid models which account for non-uniform movement are discussed, and their usefulness is assessed and illustrated by means of an example.