We show that if $\Gamma $ is a point group of $\mathbb {R}^{k+1}$ of order two for some $k\geq 2$ and $\mathcal {S}$ is a k-pseudomanifold which has a free automorphism of order two, then either $\mathcal {S}$ has a $\Gamma $-symmetric infinitesimally rigid realisation in ${\mathbb R}^{k+1}$ or $k=2$ and $\Gamma $ is a half-turn rotation group. This verifies a conjecture made by Klee, Nevo, Novik and Zheng for the case when $\Gamma $ is a point-inversion group. Our result implies that Stanley’s lower bound theorem for centrally symmetric polytopes extends to pseudomanifolds with a free simplicial automorphism of order 2, thus verifying (the inequality part of) another conjecture of Klee, Nevo, Novik and Zheng. Both results actually apply to a much larger class of simplicial complexes – namely, the circuits of the simplicial matroid. The proof of our rigidity result adapts earlier ideas of Fogelsanger to the setting of symmetric simplicial complexes.

X-ray micro-computed tomography (μCT) is a technique which can obtain three-dimensional images of a sample, including its internal structure, without the need for destructive sectioning. Here, we review the capability of the technique and examine its potential to provide novel insights into the lifestyles of parasites embedded within host tissue. The current capabilities and limitations of the technology in producing contrast in soft tissues are discussed, as well as the potential solutions for parasitologists looking to apply this technique. We present example images of the mouse whipworm Trichuris muris and discuss the application of μCT to provide unique insights into parasite behaviour and pathology, which are inaccessible to other imaging modalities.