Olivooides mirabilis from the Cambrian Fortunian Stage Kuanchuanpu Formation, in Shizhonggou section, Ningqiang County, Shaanxi Province, China. A, juvenile stage; B, prehatched development stage; C, peridermal apertural view; D–G, possible internal calyx-like polyp. Solid white dots indicate the pentaradial symmetry. Abbreviations: c, calyx; st, stalk; pe, periderm. Scale bars: A, 500 μm; B, 200 μm; C–F, 300 μm; G, 400 μm.

Quadrapyrgites quadratacris of the Cambrian Fortunian Stage Kuanchuanpu Formation, in the Zhangjiagou section, Xixiang County. A, polyp stage with uplifted peridermal aperture; B, apertural view showing concaved peridermal aperture; C, possible calyx-like polyp with a stalk. D, a 2D structure of Quadrapyrgites with simplified internal anatomy. Solid white dots indicate the pentaradial symmetry. Abbreviations: eu, exumbrella; su, subumbrella; sc, subumbrellar cavity; te, tentacle; m, mouth; pe, periderm; pa, periderm aperture; st, stalk; ca, calyx. Scale bar: 200 μm.

A, a 3D model of Quadrapyrgites; B, a reduced model of the polyp subumbrella; C, meshed computational domain and boundary conditions (dashed box in C marks the position of D).

A, B, C, and D are the velocity variations with time collected by sampling cut points in all simulations with expansion/contraction time ratios of 1:1, 2:1, 3:1, and 4:1, respectively.

Maximum flow velocity data collected by sampling cut points in all simulations with different expansion/contraction time ratios.

A, C, E, and G show the status of the polyp subumbrella at different moments. B, D, F, and H show the corresponding enlarged views of the polyp, with the white arrows representing the flow direction and velocity magnitude (the size of the arrows is proportional to the natural logarithm of the flow velocity magnitude with a range quotient of 1,000) of water flow. A, B, t = 0 s, the polyp is at rest, and the subumbrella opening is in its maximum state; C, D, t = 1.8 s, the subumbrella is in the process of expansion, and the flow velocity near the peridermal aperture has reached its maximum; E, F, t = 3 s, the subumbrella is in its maximum state, and the subumbrella opening is in its minimum state; G, H, t = 3.5 s, the subumbrella is in the process of contraction, and the flow velocity near the peridermal aperture has reached its maximum value.

Vortex visualisation of the dynamic process of Quadrapyrgite (the length of arrows was normalised to represent the orientation of velocity). A, t = 0.1 s, the upper main vortex, and the lower secondary vortex begin to form. B, t = 1s, contact between the secondary vortex and the lower boundary C, t = 2 s, the main and secondary vortex is developed to the maximum visualisation range of vorticity. D, E, t = 2.87–2.88s, separation of the main vortex occurs. F, t = 3s, the new main vortex of the contraction process formed, the expansion process ended, and the contraction process began. G, H, t = 3.9–4s, separation of the main vortex occurred. Animation supplement 1. 2D visualisation of vortex (the length of arrows was normalised to represent the orientation of flow velocity).

A, height of Quadrapyrgites. B, positions of Quadrapyrgites and cut points in computational domain.