Most Parabasalia are symbionts in the hindgut of “lower” (non‐Termitidae) termites, where they widely vary in morphology and degree of morphological complexity. Large and complex cells in the class Cristamonadea evolved by replicating a fundamental unit, the karyomastigont, in various ways. We describe here four new species of Calonymphidae (Cristamonadea) from Rugitermes hosts, assigned to the genus Snyderella based on diagnostic features (including the karyomastigont pattern) and molecular phylogeny. We also report a new genus of Calonymphidae, Daimonympha, from Rugitermes laticollis. Daimonympha's morphology does not match that of any known Parabasalia, and its SSU rRNA gene sequence corroborates this distinction. Daimonympha does however share a puzzling feature with a few previously described, but distantly related, Cristamonadea: a rapid, smooth, and continuous rotation of the anterior end of the cell, including the many karyomastigont nuclei. The function of this rotatory movement, the cellular mechanisms enabling it, and the way the cell deals with the consequent cell membrane shear, are all unknown. “Rotating wheel” structures are famously rare in biology, with prokaryotic flagella being the main exception; these mysterious spinning cells found only among Parabasalia are another, far less understood, example.