  Mapping the brain imaging data to networks, where each node represents a
specific area of the brain, has enabled an objective graph-theoretic analysis
of human connectome. However, the latent structure on higher-order connections
remains unexplored, where many brain regions acting in synergy perform complex
functions. Here we analyse this hidden structure using the simplicial complexes
parametrisation where the shared faces of simplexes encode higher-order
relationships between groups of nodes and emerging hyperbolic geometry. Based
on data collected within the Human Connectome Project, we perform a systematic
analysis of consensus networks of 100 female (F-connectome) and 100 male
(M-connectome) subjects by varying the number of fibres launched. Our analysis
reveals that the functional geometry of the common F\&M-connectome coincides
with the M-connectome and is characterized by a complex architecture of
simplexes to the 14th order, which is built in six anatomical communities, and
short cycles among them. Furthermore, the F-connectome has additional
connections that involve different brain regions, thereby increasing the size
of simplexes and introducing new cycles. By providing new insights into the
internal organisation of anatomical brain modules as well as into the links
between them that are essential to dynamics, these results also highlight the
functional gender-related differences
