**Structural design**

In contrast to conventional approaches that rely on regular building blocks, our strategy introduces irregular polyhedral building blocks by combining multiple organic subunits, wherein at least one subunit assumes a 3D coordination environment (Scheme 1d-g). As an initial implementation of this strategy, we assemble four 3-c triangular outer subunits (*C*2v symmetry) with a 4-c 3D regular or twisted tetrahedral central subunit (*T*d or *D*2d symmetry), resulting in an unconventional 8-c building unit with *D*2d symmetry and high degrees of configurational flexibility. Importantly, the topologies constructed from these *D*2d building blocks are inherently unpredictable and have likely not been reported in prior literature. In line with this concept, we design two unique building blocks, namely tetra[(3’’,5’’-diformylphenyl)phenyl] methane (TDFPM, Scheme 2a) and 3,3’,5,5’-tetra[(3’’,5’’-diformylphenyl)-bimesitylene (TDFBM, Scheme 2b). In these designs, the sp3-hybridized carbon atoms and the bimesityl groups naturally serve as regular and twisted tetrahedral central subunits respectively, while the (3’,5’-diformylphenyl) groups act as triangular outer subunits. These distinctive 8-c building blocks are subsequently condensed with *p*-phenylenediamine (PDA, Scheme 2c) as a linear linker to construct two novel 3D COFs, namely JUC-643 and JUC-644 (Scheme 2d-h), possessing unique structural characteristics and topology.

**Synthesis and characterization **

Typically, these building blocks (PDA + TDFPM/TDFBM) were dispersed in 1,4-dioxane in the presence of acetic acid, and were then heated under different reaction conditions to build JUC-643 and JUC-644, respectively (see Section S2 for details). Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) revealed the morphology of multichip for JUC-643 and cuboid for JUC-644 (Figure 1a and Supplementary Figs. 2-5). The Fourier transform infrared (FT-IR) spectra showed the appearance of new C=N stretching bands (1626 cm−1 for JUC-643 and 1624 cm−1 for JUC-644) and the disappearance of C=O (1702 cm−1 for TDFPM and 1706 cm−1 for TDFBM) and N−H (3324 cm−1 for PDA) stretching bands, manifesting the successful polymerization of aldehyde and amine (Supplementary Figs. 6 and 7). In addition, the peaks at 161 ppm for JUC-643 and 158 ppm for JUC-644 in the solid-state 13C cross-polarization magic-angle-spinning (CP/MAS) nuclear magnetic resonance (NMR) showed the presence of carbons from the imine groups (Supplementary Figs. 8 and 9). The thermogravimetric analysis (TGA, Supplementary Figs. 10 and 11) and powder X-ray diffraction (PXRD) patterns (Supplementary Figs. 12-15) revealed that both 3D COFs were stable under high temperatures (>400 °C) and in various organic solvents and acid/base aqueous solutions. The PXRD patterns of JUC-643 and JUC-644 indicate that a new crystalline phase has been formed (Supplementary Figs. 16 and 18).

**Structural determination**

According to PXRD patterns and electronic micrographs taken by SEM and TEM, JUC-644 exhibits significantly higher crystallinity than JUC-643. Therefore, the structure of JUC-644 was subjected to a detailed analysis. We used cRED technique to determine the structure of JUC-644. Sixteen individual datasets with a resolution up to 1.5 Å were collected at 99 K and the 3D reciprocal space was preliminarily reconstructed using the software *REDp*33. Unit cell of JUC-644 was firstly determined by cRED data (Figure 1c) and the reflection conditions were determined as: 0*kl*: *l*=2*n*; *h*0*l*: *l*=2*n*; *hk*0: *h*=2*n* from the 2D slices cut from the 3D reciprocal lattice, supporting the inference that space group should be *Pcca*. The unit cell (*a* = 31.669(6) Å, *b* = 17.376(3) Å, *c* = 25.285(4) Å, *α* = *β* = *γ* = 90°) and space group was confirmed by Pawley Refinement of PXRD data with software *TOPAS* 534 with *R*wp of 5.71% and *R*p of 4.13%. The cRED datasets were then processed using *X-ray Detector Software* (*XDS*)35 and six sets of them were merged by the python program package *edtools*36 to improve the data completeness. Finally, we obtained a *.hkl peaks list and fractional coordinates of all non-hydrogen atoms were determined with software *SHELXT*37. This is the lowest reported resolution of cRED data for successful structural determination using the *ab initio* methods. The final crystal structure model was obtained by the Rietveld refinement with *TOPAS* 5, with *R*wp of 9.26% and *R*p of 7.20% (Figure 1b and Supplementary Fig. 17, see Supplementary Tables 1-2 for details). The topological structure of JUC-644 is very characteristic with a 2-fold interpenetrated net, which will be discussed in detail below.

On the other hand, because of the relatively flexible structure of the 8-c building block TDFPM, the crystallinity of JUC-643 is not high enough to collect solvable X-ray or electron diffraction data. Since TDFPM and TDFBM are similar in structure, we infer that JUC-643 has the same topology with JUC-644. A non-interpenetrated net in space group *Pba2* (No.32) optimized by the *Material Studio*38 software package matches well with the PXRD pattern (Supplementary Fig. 19). Pawley refinement was applied to PXRD data and showed low residual factors (*R*p = 2.00%, *R*wp = 2.90%, Supplementary Fig. 20, see Supplementary Table 3 for details). In addition, we also tried alternative structures, such as non-interpenetrated **bcu**, **dmf**, and **xux** net for JUC-643 and their simulated PXRD patterns did not match the experimental result (Supplementary Figs. 21-23, see Supplementary Tables 4-6 for details). All of the evidence above strongly confirms our inference that the structure of JUC-643 is the non-interpenetrated net with the same topology as JUC-644.

Notably, both 3D COFs displayed mesoscopic double helical structures, an extremely uncommon occurrence in COF structures39. The helices of JUC-643 are generated by condensation of the adjacent 8-c building blocks with two PDA linkers along *b*-axis. Two spirals are linked at the sp3 hybridized carbon atom of the geometric center of TDFPM and they further propagate along [010] direction (Figure 2a, 2c and Supplementary Fig. 24). Similarly, the dual helices of JUC-644 are generated by the alignment of adjacent 8-c building blocks with two PDA linkers along the* b*-axis. The two helices are connected by C-C bonds at the geometric center of the TDFBM motif and further propagate along [010] direction (Figure 2b, 2d and Supplementary Fig. 25). Both COFs are in achiral space groups because the helices appear in pairs in both structures and the whole frameworks are racemic.

As mentioned above, non-penetrated JUC-643 is in non-centrosymmetric *Pba*2 while 2-fold interpenetrated JUC-644 is in centrosymmetric *Pcca*. *Pba2* is a *translationengleiche* subgroup of *Pcca* in *mm*2 Laue group by removing the *c*-glide plane along [010] direction, which means the interpenetration of JUC-644 is completed by 180° rotation around the *a- *or* c-*axis rather than simple translation to form the center of symmetry in the structure (Figure 2e and 2f). This is similar to the interpenetration mode in the ZOF structure, in which two **crb** nets are interpenetrated by 90° rotation19.

**Topological analysis**

Although the structures of both COFs have been determined, their topologies cannot be defined easily. According to traditional topological analysis methods, the whole building block in COFs is always regarded as a vertex. Under this deconstruction method, the structures are surprisingly in a [6(+2)]-c **pcu**-like topology: every 8-c building block is connected with 6 neighbors along 3 mutually orthogonal directions and there are 2 PDA linkers between neighboring building blocks along the direction parallel to the helices and 1 PDA along the other directions. This implies that adjacent building blocks are connected by multiple links, forming the double helical structure mentioned above, which is unreported in all known 3D COF structures (Scheme 1e and 1f). Keeping considering the topology as a [6(+2)]-c **pcu** net is unreasonable because the “double links” parts are oversimplified to 1D and unable to accurately describe the porous and helical structures generated by the multiple links. This is also a subversive counter-example for the traditional topological analysis method of COFs, indicating that the entire building block cannot always be taken as a single topology vertex.

To precisely describe the topology of JUC-643 and JUC-644, we divided the 8-c building block into a 4-c vertex located in the center of the tetrahedron and four 3-c vertices in the center of the benzene ring of 3',5'-diformylphenyl group (Scheme 3a). In other words, the structure is deconstructed to a [4+3(+2)]-c net according to the position of the subunits rather than a [6(+2)]-c net according to the whole building block (Scheme 1g and 3b-d). The deconstruction process was completed using the software *Material Studio* manually and using software *ToposPro*40 by automatically clustering, and both resulting topologies were analyzed and proven to be identical based on vertex symbols and td10 values* *(see Supplementary Table S7 for details). The result topology was further analyzed by program *Systre*41, showing the highest space group symmetry of the topology is in *Pban* (No.50). The topology is different from all the contents in the *RCSR* database42, which means it is a completely unprecedented topology.

Another intriguing aspect of the new topology is that the projection patterns along and directions are identical (Supplementary Fig. 26), suggesting the structure has a good chance to be related to tetragonal symmetry. The cell parameter was set to be *a*=*b* to make a tetragonal cell, and 3-c vertices' fractional coordinates were set to be *x*=*y* to make them on the diagonal of the *xOy* plane. The resulting vertex-only structure is obviously in tetragonal symmetry, but the helical edges along the *c* axis break the *C4* axis of rotation (Supplementary Fig. 27a and b). A tetragonal [4+4]-c topology in space group *P*4/*nbm* (No.125, a minimal *translationengleiche* supergroup of *Pban*) can be accordingly defined by completing the edges along the *c* axis, which is also an unprecedented topology. The relationship between mentioned [4+4]-c and [4+3]-c topologies is similar to that between **pcu** and **cds** (Supplementary Fig. 27c and d). Deleting part of edges along specific directions would reduce the topological symmetry.

Derived topologies in 4-c structures can be defined by dividing a 4-c vertex into two 3-c vertices. For instance, **dmd**, **dmg**, **dmh**, **sur**, **tfi** and **tfk** are derived from **pts** by splitting tetragonal or square vertices along different directions. The twisted tetrahedral vertex in JUC-644 can be split into two triangular vertices defined in the center of the mesitylene ring, forming a novel [3+3]-c topology. This is the third new topology discovered in this work. The highest space group of this [3+3]-c topology is also *Pban*. In descending order of symmetry, the new-found [4+3]-c, [4+4]-c, and [3+3]-c topologies are respectively named as **jca**, **jcb** (**jcb** stands for Jilin University China-b) and **jcc **(**jcc** stands for Jilin University China-c, Scheme 3e and Supplementary Fig. 28, see Supplementary Tables 7-9 for details). Comparison of **jca**, **jcb**, and **jcc** with other similar topologies in *RCSR* database42 is detailed in Supplementary Table 10 and Figs. 29 and 30.

The discovery of three new topologies indicates the success of our synthetic strategy. Notably, the number of vertices in **jca**, **jcb** and **jcc** topologies is not inversely proportional to their connected numbers, but is determined by the design of 8-c building blocks. This means the quantity ratio of topological vertices in COF structures can be defined manually by controlling the central and outer subunits ratio. For the *D*2d 8-c building block itself reported in this article, more COFs in different topologies may be designed by adjusting subunits' orientation and steric hindrances, and by connecting the building blocks to linkers with various configurations and coordination numbers. Furthermore, new topologies can also be designed and discovered by altering the geometry of central or outer subunits to tetrahedrons, pyramids, prisms or more complicated shapes. Building blocks may be even composed of multiple central subunits and different types of outer subunits, producing more possibilities for new topologies. The core requirement of this strategy is at least one subunit should be in 3D coordination environment, making the building block in irregular polyhedrons with high degrees of configurational freedom.** **

**Porosity analysis**

The nitrogen (N2) adsorption and desorption isotherms were performed to determine the porosity of both COFs at 77 K. As illustrated in Supplementary Fig. 31 and Figure 1d, JUC-643 and JUC-644 exhibit a sharp gas uptake at low pressure (*P*/*P*0 < 0.1) demonstrating their microporous nature. The inclination of isotherms in the pressure (*P*/*P*0) range of 0.8 to 1.0 and slight desorption hysteresis for JUC-643 can be attributed to the presence of textural mesopores from the agglomeration of COF crystals. These two COFs both show microporous cavities and the measured pore sizes are 1.2 nm, 1.9 nm, and 1.5 nm along *a*,* b*, and *c* axis for JUC-643 and are 0.7 nm, 1.0 nm, and 1.0 nm along *a*,* b*, and *c* axis for JUC-644 (Supplementary Figs. 32-37). Their theoretical pore size distributions calculated by the nonlocal density functional theory (NLDFT) also revealed micropores with the pore sizes of 1.21, 1.81, and 1.43 nm for JUC-643, and 0.71 and 0.98 nm for JUC-644 along different axis (Supplementary Fig. 38 and Figure 1e), perfectly fitting on the proposed models. The pore size data provided additional support for the non-interpenetrated structure of JUC-643, establishing its topological congruence with that of JUC-644. Respectively, the Brunauer-Emmett-Teller (BET) surface area for JUC-643 and JUC-644 is 1464 m2 g-1 and 2771 m2 g-1 respectively (Supplementary Figs. 39 and 40).

**Gas adsorption and separation**

The novel porous structure and high surface area of JUC-644 provide promising potential for gas adsorption and separation. In this regard, we investigated the adsorption characteristics of JUC-644 towards various light hydrocarbon molecules. Single-component adsorption isotherms of C2H6, C3H8, and *n*-C4H10 on JUC-644 were measured at three different temperatures: 283 K, 298 K, and 313 K (Figure 3a, 3b, and Supplementary Figs. 41-43). Our results reveal that JUC-644 exhibits higher adsorption capacities for C2H6, C3H8, and *n*-C4H10 compared to JUC-643 at 298 K (4.83, 11.28, 10.45 mmol g−1 in JUC-644 and 1.23, 2.47, 3.32 mmol g−1 in JUC-643 respectively), demonstrating the highest C3H8 and *n*-C4H10 adsorption uptake among all porous materials, surpassing values reported for C3H8 in BSF-1 (1.94 mmol g−1)43, PAF-40-Fe (2.58 mmol g−1)44, and g-C3N4@Zr–BPDC (8.90 mmol g−1, Figure 3c and Supplementary Table 11)45, as well as outperforming values reported for *n*-C4H10 in NaX zeolite (1.56 mmol g−1)46, Zn-BTM (2.01 mmol g−1)47, and Zn-ZIF-8 (4.69 mmol g−1, Figure 3d and Supplementary Table 12)46. The *n*-C4H10 isotherms of JUC-644 exhibited a slightly steeper increase compared to C3H8, and both were considerably steeper than the C2H6 isotherm. This indicates that the framework affinity of JUC-644 for guest molecules follows the order of *n*-C4H10 > C3H8 > C2H6.

The Clausius−Clapeyron equation48 is utilized to calculate the isosteric heat of adsorption (*Q*st) values for *n*-C4H10, C3H8, and C2H6 at near-zero loading, yielding values of 56, 41, and 29 kJ mol−1, respectively (Figure 3e, see Supplementary Tables 13-15 for details). This outcome aligns with the observed lower uptake and more gradual isotherms for C2H6, indicating a high adsorption selectivity for *n*-C4H10/C2H6 and C3H8/C2H6. The ideal adsorbed solution theory (IAST) selectivity49 parameter is paramount in assessing materials' adsorption and separation efficiency. Within the 0-100 kPa range, the *n*-C4H10/C2H6 selectivity of JUC-644 exhibits an increasing trend, while the C3H8/C2H6 selectivity initially decreases and then increases. The maximum values of the selectivity of *n*-C4H10/C2H6 and C3H8/C2H6 at 100 kPa are 79.2 and 10.4, respectively (Figure 3f and Supplementary Figs. 44-52, see Supplementary Tables 16-19 for details).

**Density-functional theory (DFT) calculations**

In order to investigate the interaction between gas molecules and the channels, *ab initio* molecular dynamics (AIMD) simulations were carried out using the CP2K software, employing DFT as the computational method50-51. We initially positioned the gas molecules at the center of the channels and simulated their trajectory changes at 298.15 K. As is shown in Supplementary Fig. 53 and the GIF images in attaching files, during the process of simulation, the color of the guest molecules transitioned from blue to white, and then to red (the blue-to-white transition represents the adsorption process of gas molecules from the center of the channels to the channel walls, while the white-to-red transition represents the thermal motion trajectory of the molecules after adsorption within the channels). It can be observed that the white-to-red trajectories of C2H6 and C3H8 show clear separation, indicating weaker restrictive effects of the COF channels on these two gas molecules. The thermal motion within the channels is relatively facile for these molecules, resulting in faster diffusion. Furthermore, examining the positions of the white-to-red trajectories of C2H6 and C3H8, it is evident that the white-to-red trajectory of C2H6 is closer to the center of the COF channels, indicating weaker interaction between C2H6 and the channels, thus facilitating easier diffusion within the channels (Supplementary Fig. 53a-f). In contrast, the white-to-red trajectory of *n*-C4H10 largely overlaps, and even partially overlaps with some blue trajectories, suggesting stronger restrictive effects of the COF channels on this molecule (Supplementary Fig. 53g-i). Consequently, the thermal motion and diffusion of *n*-C4H10 within the channels are relatively restricted, leading to slower diffusion.

**Breakthrough experiment**

The substantial disparity in adsorption capacities between C2H6 and longer alkanes suggests the promising potential of JUC-644 for recovering C2H6 from NGLs. The recovery of C2H6 from NGLs is a significant source of industrial C2H6, which is a primary raw material for C2H4 production52,53. Nevertheless, conventional cryogenic distillation and solvent absorption methods employed for gas separation are characterized by their high energy consumption and detrimental environmental impact. In light of these inherent shortcomings, adsorption separation has emerged as a promising and sustainable alternative, offering energy efficiency and environmental friendliness54,55. A key aspect of this approach lies in developing porous materials possessing exceptional adsorption capacity and separation selectivity56,57. Although MOFs have gained considerable attention in the realm of light hydrocarbon separation58-60, their practical utilization in this context has been impeded by their relatively lower adsorption capacities for C3H8 and *n*-C4H10 at ambient temperatures, as well as their inadequate stability under humid conditions. Addressing these limitations, JUC-644 stands out as an exceptional porous adsorbent, perfectly suited for ethane recovery from NGLs.

We initially tested the separation performance of JUC-644 in C2H6/C3H8 and C2H6/*n*-C4H10 (1:1, Tfr: 2 mL min-1) mixtures. The results revealed that in the C2H6/C3H8 mixture, the retention times for C2H6 and C3H8 were 73.8 min g−1 and 183.6 min g−1 (Figure 4a and Supplementary Figs. 54 and 55). In the C2H6/*n*-C4H10 mixture, the retention times for C2H6 and *n*-C4H10 were 61.9 min g−1 and 220.5 min g−1, respectively (Figure 4b and Supplementary Figs. 56 and 57). To validate the practical application of JUC-644 in C2H6 recovery from NGL, we also conducted separation tests on a C2H6/C3H8/*n*-C4H10 (46:34:20, v/v/v, Tfr: 5 mL min-1) mixture at 298 K. The results demonstrated that C2H6 rapidly passed through JUC-644 with a retention time of 29.2 min g−1, while C3H8 and *n*-C4H10 exhibited retention times of 73.8 min g−1 and 162 3 min·g−1, respectively (Figure 4c and Supplementary Figs. 58 and 59). The yield of C2H6 (purity >99.99%) was 4.73 mmol g−1. Furthermore, breakthrough experiments were performed under moist conditions (~50% relative humidity). The retention times of C3H8 and *n*-C4H10 remained relatively unchanged (73.1 min g−1 and 157.2 min g−1, respectively) in the presence of water (Supplementary Figs. 60 and 61). Additionally, the performance of JUC-644 was verified through five consecutive separation cycles, demonstrating its sustained separation efficiency (Figure 4d). These results confirm that JUC-644 is a promising material for efficient and environment-friendly recovery of C2H6 from NGLs.