Motifs in architecture, mathematics and nature have inspired chemists to create their molecular counterparts1,2,3,4,5,6,7,8,9. Buckminsterfullerene (C60)1, for instance, structurally resembles the geodesic dome by Buckminster Fuller. Fuller also conceived of face-rotating polyhedra (FRP)10, wherein each face of a polyhedron rotates around its central axis, transferring the two-dimensional (2D) chirality of the faces into the 3D chirality of the polyhedron (Fig. 1a). In mathematics, chirality transfer in FRP is highlighted as an analogous strategy to construct polyhedral dice11. In life sciences, some virus capsids can be regarded as FRP12,13,14,15, in which each face of the icosahedral cricket paralysis virus capsid contains three quasi-equivalent subunits that form identical rotational directionality (Fig. 1b)14. The transfer of 2D chirality of the building block to 3D chirality in FRP through self-assembly can be regarded as a type of emergent property16,17,18.

Figure 1: 3D chiral polyhedra originated from 2D chiral facial units.
figure 1

(a) Synergetic interactions between the rotating triangular faces in a polyhedron proposed by Buckminster Fuller. (b) All subunits of icosahedral cricket paralysis virus have identical rotational directionality. (c) Truxene building block shown as a ball-and-stick model (red and blue, carbon; white, hydrogen; yellow, oxygen; green, butyl group); its rotation patterns are considered to be either clockwise (C) or anticlockwise (A) when viewed vertical to the aromatic plane. By reacting with ethylene diamine to form an octahedron, the truxene fragment loses its mirror symmetry and becomes a rotational face.

Inspired by mathematics19 and the structures of virus capsids20, chemists have synthesized molecular polyhedra with various sizes and shapes through self-assembly. Most of these polyhedra are highly symmetric and achiral20,21,22,23,24,25, and chiral molecular polyhedra with lower symmetry have attracted more and more attention because they increase the complexity of motifs and may bring more sophisticated functions26,27,28,29,30,31. Generally, the construction of chiral molecular polyhedra follows two strategies: to use predetermined 3D chiral building blocks as the edges30,32, vertices33,34 or faces35,36 of polyhedra to transfer 3D chirality of the components to the 3D chirality of the chiral structures, or to use achiral components to generate chiral metal-organic polyhedra37,38,39,40,41,42 during a self-assembly process. The latter approach relates to symmetry breaking, and investigation of the process of such complex molecular self-assembly may help to elucidate the evolution of matter towards complexity43. However, metal-organic polyhedra remain the dominant type of chiral molecular polyhedra assembled from achiral components, and the resolution of the mixed racemic structures as well as scrutiny of the intermediates and the formation mechanism are challenging.

Here we report a strategy to assemble a C3h-symmetric building block into purely organic FRP (Fig. 1c) through dynamic covalent chemistry44,45,46. The building block loses its σh mirror symmetry in the polyhedra and brings either a clockwise (C) or an anticlockwise (A) rotation around the centre of each face, thus generating a series of FRP stereoisomers. Our thermodynamic polyhedra exhibit homo-directionality, which resembles the identical rotational directionality of each facial unit in some virus capsids. We also investigated the formation mechanisms of the FRP from rotational facial units based on their high spectral sensitivities. The non-covalent interaction among faces has been suggested to be the primary reason for the facial homo-directionality.


Synthesis of FRP 1 with achiral vertices

The facial building block TR (Fig. 1c and Supplementary Fig. 1) consists of a rigid planar 10,15-dihydro-5H-diindeno[1,2-a;10,20-c]fluorine (truxene) core47,48, six alkyl chains at central positions to increase solubility and prevent aggregation, and three carboxaldehyde groups at peripheral positions for reversible imine formation. This building block was readily synthesised from truxene in three steps with high yields (Supplementary Fig. 2).

The truxene building block (TR) (4 eq) and ethylene diamine (EDA) (6 eq) were reacted in toluene with catalytic amounts of trifluoroacetic acid (TFA) at room temperature, affording TR4EDA6 octahedron 1 in high yield. The mass spectrum of 1 confirmed that it was formed exclusively in solution and exhibited a molecular weight (M.W.) of 3196.29 daltons (calculated M.W.: 3196.31), corresponding to a [4+6] composition (Fig. 2a).

Figure 2: Molecular structure and characterisation of octahedra 1.
figure 2

(a) Molecular structure of the octahedron (CCCC)-1. (b) Single-crystal structure of the co-crystal of (CCCC)-1 and (AAAA)-1 (hydrogen atoms and butyl groups are omitted for clarity). (c) Chiral HPLC spectrum contains two peaks corresponding to (AAAA)-1 and (CCCC)-1 in a 1:1 ratio. The absorbance for all octahedra was recorded at 325 nm. (d) Experimental and (ZINDO/S)-predicted (the insert) CD spectra of (AAAA)-1 (red), (CCCC)-1 (blue), and the unseparated racemic mixture (black) in hexane.

Single-crystal characterization of FRP 1

Single crystals were grown by diffusing hexane into the toluene solution of 1. Single-crystal X-ray diffraction analysis revealed that 1 has a tetra-capped octahedral structure21,33, in which four truxene units occupy four faces linked by six diamine units in the vertices (Fig. 2b). Truxene is achiral in three dimensions because of the presence of a mirror symmetry, and chiral in two dimensions because the three sp3 carbons of the truxene core form a rotating pattern along the C3 axis in either a clockwise or an anticlockwise direction (Fig. 1c), similar to the pattern in some virus capsids. Therefore, the truxene fragment loses its mirror symmetry in a polyhedron and becomes a rotational face, resulting in five possible stereoisomers for 1; these configurations are named after the directionalities of the exterior faces as CCCC and AAAA (homo-directional with T symmetry), CCCA and CAAA (hetero-directional with C3 symmetry) and CCAA (hetero-directional with S4 symmetry) (Supplementary Fig. 1). We measured more than five single crystals of 1, and found all of them were the co-crystallization of only the T-symmetric enantiomers (i.e., (CCCC)-1 and (AAAA)-1) packed in the P-1 triclinic space group (Fig. 2b). No other diastereomers or self-sorting of the two enantiomers into two enantiopure crystals was observed. All imine bonds are E conformers, locating in the conjugated plane and rotating in the same direction as the sp3 carbons of the truxene core. The butyl groups compacted inside the octahedra distort the terminal carbons, whereas the butyl groups that stretch outside remain linear.

NMR characterization of FRP 1

The nuclear magnetic resonance (NMR) spectra of 1 (Supplementary Figs 3–9) are consistent with its single-crystal structure. The 1H NMR spectrum (Fig. 3) reveals only a single set of peaks for all twelve sets of protons on the truxene backbones (Ha, Hb, and Hc) and imines (Hd), suggesting that these protons are individually interchangeable through twelve symmetry operations49. Therefore, only the T-symmetric stereoisomers of 1 exist in solution. All butyl protons inside the octahedron are more shielded from the three neighbouring truxene units than those outside. The 2D NMR spectra allowed for the assignment of each proton and carbon of octahedron 1. In addition, the nuclear Overhauser effect (NOE) crosspeak between imine protons Hd and Hb (instead of Hc) suggests that all imine bonds rotate in the same direction as the sp3 carbons of the truxene core in solution, and the crosspeak between Hd and He1 reflects the shape-persistency and rigidity of the octahedron 1 in solution (Fig. 3, insert).

Figure 3: 1H NMR and NOE spectra of octahedron 1.
figure 3

1H NMR spectrum was measured in dichloromethane and fully rationalised by matching the crystal structure and 2D NMR spectra. The inserted NOE spectrum exhibits the crosspeaks of Hd–Hb and Hd–He1, suggesting Hd is spatially close to Hb and He1 in solution, as presented in the molecular structure (only one butyl chain is shown for clarity).

Chiral-HPLC and CD characterizations of FRP 1

Further application of chiral high-performance liquid chromatography (HPLC) and circular dichroism (CD) spectroscopy confirmed that, among all possible stereoisomers, only (CCCC)-1 and (AAAA)-1 exist in a 1:1 ratio both in crystal and in solution (Fig. 2c). The solution of crude 1 gives no detectable CD signal. In contrast, the CD signal of the separated octahedron eluting at 4.6 min gives a strong negative signal in the truxene absorption region (340 nm), whereas the fraction at 5.9 min provides a mirror-like positive signal (Fig. 2d). The CD signals of both separated octahedra have a molar ellipticity of 4.6 × 106 deg cm2 dmol−1, which, to our knowledge, is the largest molar ellipticity ever reported50 and is substantially larger than that of helicene (ca. 3.5 × 105 deg cm2 dmol−1)51. We attribute this large molar ellipticity to the high molar absorptivity of truxene and to the rigid geometry of the octahedra. The CD spectrum of the octahedron at 4.6 min matches the (ZINDO/S)-predicted CD spectrum of (AAAA)-1, and the CD spectrum at 5.9 min corresponds to (CCCC)-1 (Fig. 2d, insert).

Synthesis and characterizations of FRP 2 with chiral vertices

After achieving homo-directionality of each face of the molecular polyhedra, we attempted the enantioselective assembly of FRP, similar to the assembly observed in nature for some virus capsids12,13,14,15. Inspection of the single-crystal structure of 1 revealed that all EDA vertices of (AAAA)-1 are in a gauche conformation, and the two amino groups have a torsion angle of ca. −60°, which is the same torsion angle between the amino groups in (R,R)-diaminocyclohexane (CHDA) (Supplementary Fig. 10). Similarly, the amino groups in the vertices of (CCCC)-1 and (S,S)-CHDA exhibit a torsion angle of ca. 60°. Therefore, we envisioned that the conformational preorganisation of diamines in (R,R)-CHDA or (S,S)-CHDA would dominate the facial directionality of the octahedra.

Under the same conditions as those used to prepare 1, (R,R)-CHDA and TR were reacted at room temperature for 24 h. The mass spectrum of the product suggested the exclusive formation of TR4CHDA6 with a M.W. of 3520.52 (calculated M.W.: 3520.59), corresponding to octahedron 2. However, the 1H NMR spectrum exhibited eleven signals for the imine protons (Hd), indicating a mixture of diastereomeric octahedra with all three symmetries, T, C3 and C2 (Supplementary Fig. 11a). HPLC analysis revealed a distribution of three diastereomers, which eluted at 10.3 min (42%), 14.9 min (42%) and 24.1 min (14%) (Fig. 4a). We isolated each diastereomer and determined its symmetry through the number of imine signals in the NMR spectra. The T-, C3-, and C2-symmetric diastereomers that eluted at 10.3, 14.9, and 24.1 min gave rise to a single Hd signal, four Hd signals and six Hd signals, respectively (Supplementary Figs 11–14). The C2-symmetric diastereomer (CCAA)-2 partially converted into other diastereomers after 24 h, thus suggesting that it is a kinetic product. To convert all kinetic products to their corresponding thermodynamic products, we heated 2 at 110 °C for 48 h after stirring at room temperature for 24 h. HPLC and NMR analyses indicated the near quantitative transformation to the T-symmetric diastereomer, which eluted at 11.2 min (Fig. 4a and Supplementary Fig. 11b).

Figure 4: Characterisation of octahedra 2.
figure 4

(a) Chiral HPLC spectra of the kinetic products of 2 synthesised at 25 °C (top) revealing three diastereomers (i.e., (AAAA)-2, (CAAA)-2 and (CCAA)-2) that changed into the thermodynamic product (AAAA)-2 when heated at 110 °C for 48 h (bottom). (b) Experimental and (ZINDO/S)-predicted (the insert) CD spectra of (AAAA)-2 (red), (CAAA)-2 (blue) and (CCAA)-2 (green) in hexane. (c,d) Single-crystal structures of the thermodynamic (AAAA)-2 (c) and kinetically stable (CAAA)-2 (d) (hydrogen atoms and butyl groups are omitted for clarity).

On the basis of single-crystal X-ray diffraction analysis, we confirmed the T- and C3-symmetric diastereomers to be (AAAA)-2 and (CAAA)-2 octahedra, respectively (Fig. 4c,d). The chirality of the octahedra was inherited from that of the (R,R)-CHDA vertices. As in (AAAA)-1, all imine bonds in (AAAA)-2 and the A faces of (CAAA)-2 rotate towards the sp3 carbons of truxene, whereas the A face of (AAAA)-2 rotates against the sp3 carbons to match the gauche conformation of the diamine vertex. This response in the imine arrangements to the directional change of the truxene faces is rare, presumably due to the rigidity in the diamine vertices, truxene skeletons and imine junctions.

The structural change in these diastereomers also leads to significantly different spectroscopic results. The CD spectra of (AAAA)- 2, (CAAA)- 2 and (CCAA)-2 are similar to but sequentially weaker than that of (AAAA)-1, consistent with the (ZINDO/S)-predicted CD spectra (Fig. 4b, insert). This trend can be rationalized by the decrease in the alternate angles of the truxene cores (Supplementary Fig. 15).

As expected, the enantiomeric vertex of (S,S)-CHDA led to enantiomeric formation of the thermodynamic octahedron (CCCC)-3 through the (CCCA)-3 and (CCAA)-3 kinetic octahedra (Supplementary Fig. 16).

Kinetics of the synthesis of FRP 2

The formation of octahedron 2 at 298 K constitutes a kinetically controlled dynamic combinatorial library6,46. Therefore, we monitored the library, which contained 1.6 mM TR, by time-dependent chiral-HPLC-MS, UV–vis and CD to investigate the possible mechanistic pathways6,52,53 (Fig. 5). In 5 min, most of the TR reacted with diamine to form the [1+1] and [1+2] intermediates, which gave rise to a negligible CD signal. In 25 min, the reaction generated more [3+3], [3+4], and [4+5] intermediates, which exhibited a strong CD signal. All intermediates disappeared at 60 min except for the [4+5] intermediate, which gradually transformed into the [4+6] octahedra after 24 h. At room temperature, the formation and cleavage of an imine bond is fast but the transformation from the kinetic (CAAA)-2 and (CCAA)-2 to the thermodynamic (AAAA)-2 was extremely slow. Therefore, we postulated that the cyclohexyl group of CHDA shields the imine bonds in the octahedral ‘testudo formation’ in a cooperative manner.

Figure 5: Time-dependent characterisation of the synthesis of octahedron 2.
figure 5

(a) Selected HPLC spectra at certain time intervals. The components of the intermediates were determined by mass spectrometry. (b) Kinetic profile of the synthesis of octahedron 2 (1.6 mM at 298 K, absorption monitored at 325 nm), showing the consumption of truxene and the formation of three octahedral diastereomers. The formation and disappearance of the intermediates with the [1+1], [1+2], [3+3], [3+4] and [4+5] components can also be tracked. The percentages were evaluated from the HPLC peak areas. (c) Time-dependent CD intensities at 340 nm normalised by the intensity at 24 h.

Reasons for the facial homo-directionality in FRP 1 and 2

To shed light on the homo-directionality of the CCCC or AAAA configuration of all thermodynamic products of octahedra 1, 2 and 3, we calculated the free energies of different stereoisomers by the Compass II force field. The (CCCC)-1 and (AAAA)-1 enantiomers had the lowest energies among all stereoisomers of 1, whereas the enantiomeric production of (AAAA)-2 and (CCCC)-3 can be rationalized by their relative energies being the lowest among all stereoisomers of 2 and 3 (Table 1). In addition, the energy differences among the diastereomers were primarily due to non-covalent contacts and repulsion forces of the butyl groups inside the octahedra. For illustration, the energy of (AAAA)-1 was calculated to be 12.2 kcal mol−1 lower than that of (CAAA)-1, in which 9.7 kcal mol−1 was attributed to the difference in van de Waals interaction. This phenomenon is correlated to the crowded interior of the octahedra in the crystal structures, as well as in the simulated structures (Supplementary Fig. 17). Therefore, we speculate that the non-covalent repulsion forces among the interior butyl groups are essential for directing the homo-directional facial rotations of the thermodynamic polyhedra.

Table 1 Energies of octahedra 1 and 2 calculated with COMPASS II force field.


We introduced 2D chiral truxene building block to generate a series of 3D chiral polyhedra with rotational faces. The homo-directionality in our thermodynamic polyhedra resembles the identical rotational directionality of each facial unit in some virus capsids. By controlling the vertex, we stereoselectively synthesised thermodynamic homo-directional FRP and kinetic hetero-directional products. This strategy could be extended to other multifarious 2D asymmetric molecules to produce more complex Platonic and Archimedean polyhedra, which could be used for molecular recognition, chiral separation or asymmetric catalysis. We anticipate our assay to be a starting point towards more sophisticated molecular polyhedra with rotational faces, providing a strategy to mimic the sophistication of viruses.


Synthesis of the FRP

Vicinal diamine (6 eq) in anhydrous toluene and TFA (0.025 eq) were added to a schlenk flask (1 l) and stirred until dissolved. TR (4 eq) in toluene (400 to 600 ml) was added dropwise to the flask within 24 h. The solution was kept stirring for another 24 h. Solvents were evaporated under vacuum and solid was used for chiral separation and crystal growth without further purification. General experimental information and characterization details can be found in the Supplementary Methods.

NMR and MS characterization

1H and 13C nuclear magnetic resonance (NMR) spectra were recorded on a Bruker AVIII-500 spectrometer (500 and 125 MHz, respectively) or Bruker AVIII-850 spectrometer at 298 K (850 and 213 MHz, respectively) and are reported relative to residual solvent signals. Matrix-assisted laser desorption/ionization time of flight mass spectra (MALDI-TOF MS) were collected on a Bruker microflex LT-MS with 2,4,6-trihydrotyacetophenane (0.05 M in methanol) as matrix. High-resolution mass spectra (HRMS) were collected on a Bruker En Apex Ultra 7.0T FT-MS.

Single-crystal X-ray diffraction

Single crystal X-ray diffraction data were collected on Rigaku SuperNova X-Ray single crystal diffractometer using Cu Kα (λ=1.54184 Å) micro-focus X-ray sources at 100 K. The raw data were collected and reduced by CrysAlisPro software, the structures were solved by SHELXS or SHELXT and refined by SHELXL. Solution and refinement procedures are presented in the Supplementary Methods and specific details are compiled in Supplementary Table 1 and Supplementary Figs 18–22. Crystallographic information files are provided as Supplementary Data (Supplementary Data 1 for 1, Supplementary Data 2 for (AAAA)-2, Supplementary Data 3 for (CAAA)-2, Supplementary Data 4 for (CCCC)-3, Supplementary Data 5 for (CCCA)-3).

HPLC and CD characterization

HPLC analyses were performed on a Shimadzu LC-16A instrument, using Daicel Chiralcel IE Columns. FRP 1 was separated by HPLC in the mobile phase of hexane:ethyl acetate=83:17 (v/v) with 0.1% diethylamine, and FRP 2 was separated in the mobile phase of hexane:ethanol=75:25 (v/v) with 0.1% diethylamine. CD spectra were collected on JASCO J-810 circular dichroism spectrometer at 298 K. All CD spectra of the separated enantiomers were measured in hexane.

Kinetics of the synthesis

TR (122 mg, 0.160 mmol), (R,R)-CHDA (14.4 mg, 0.240 mmol) and TFA (1.37 mg, 0.0120, mmol) were reacted in toluene (100 ml) at 298 K. At certain time intervals, the reaction solution were drawn out and measured by HPLC in the mobile phase of hexane:ethanol=75:25 (v/v) with 0.1% diethylamine. The experimental details are presented in the Supplementary Methods and HPLC spectra are compiled in Supplementary Figs 23–35.

Computational methods

All the structural optimization and energy calculation were carried out in Materials Studios 7.0 by using the COMPASS II force field. The CD spectra were calculated at ZINDO semi-empirical level with Gaussian 09. Details of the method are provided in the Supplementary Methods. Coordinates of all optimized structures are provided in Supplementary Data 6.

Data availability

Crystallographic data in this study were deposited at the Cambridge Crystallographic Data Centre with the accession codes (CCDC 1063965, 1406534, 1406540, 1406657, and 1407221). The authors declare that all other data supporting the findings of this study are available within the article and its Supplementary Information files or available from the authors upon reasonable request.

Additional information

How to cite this article: Wang, X. et al. Assembled molecular face-rotating polyhedra to transfer chirality from two to three dimensions. Nat. Commun. 7:12469 doi: 10.1038/ncomms12469 (2016).