Natural images exhibit strong geometric regularities: local structures, such as edges, corners, and textures, appear in many orientations and mirror configurations. Since Vision Transformers (ViTs) operate on square image patches, these transformations naturally correspond to the dihedral symmetry group
D8, also known as the octic group. Recent work has shown that ViTs can be made reflection equivariant and more efficient than standard ViTs simultaneously by implementing the linear layers in the Fourier domain of the reflection group. In this work, we extend the equivariance to reflections and rotations and analyze the scalability of the resulting networks. Our Quick ViTs, based on octic equivariant linear layers, achieve 5.33x reductions in FLOPs and up to 8x reductions in memory compared to ordinary linear layers. By analyzing the arithmetic intensity of these layers, we identify theoretical limits on how much the FLOP savings translate into throughput improvements on modern GPUs. However, these limitations disappear as the embedding dimensions increase. Enabled by their computational efficiency, we conduct a broader empirical evaluation of equivariant ViTs than in previous work. Upon training supervised (DeiT-III) and self-supervised (DINOv2) on ImageNet-1K, we find that our Quick ViTs match or exceed baseline accuracy while at the same time providing substantial efficiency gains.