**Holy Pentagon: From Mathematics to Chemistry and**** ****Material Science**

*Pentagon-based 2D materials have received increasing attention because of their unique atomic configurations, rich physical and chemical properties, and their promise for broad applications. The theoretical prediction of penta-graphene [1] together with the finding of the 15 ^{th} type of pentagons that can tile a plane with no overlaps or gaps highlight the geometry-driven discoveries in science.*

Pentagon is well-known to mathematicians for the golden ratio (0.618) and the fifth Platonic solids, the dodecahedron composed of 12 pentagonal faces. In the last two decades, the mathematical pentagon-based geometric models have been introduced to practice in chemistry and materials science, leading to the discoveries of many pentagonal molecules and pentagon-based 2D structures and materials. For instance, the synthesized pentagonal molecules include pentalene (C_{8}H_{6}) [2], acepentalene (C_{10}H_{6}) [3], octathio circulene (C_{16}S_{8}) [4], five-membered sulfur–pnictogen ring SN_{2}P_{2}[5], and aromatic pentagonal anion P_{2}N_{3}^{–}[6].

In 2015, based on extensive theoretical simulations, we proposed a 2D carbon allotrope composed entirely of pentagons, penta-graphene, which has a 2D projection resembling the famous 2D pattern named Cairo pentagon tiling. Although penta-graphene is metastable thermodynamically compared to graphene, it is dynamically and mechanically stable, and can withstand high temperatures up to 1000 K. The thermodynamic stability of penta-graphene over the synthesized smallest fullerene C_{20} implies that it could be realized experimentally. Due to the exotic atomic configuration, penta-graphene exhibits an array of intriguing properties, such as negative Poisson’s ratio and ultrahigh ideal strength that can even outperform graphene. More interestingly, penta-graphene can be either rolled up to form 1D pentagon-based nanotubes or stacked to form 3D stable structures. Penta-graphene and its derivatives exhibit great potential for applications in nanoelectronics and nanomechanics.

Inspired by the prediction of penta-graphene, tremendous attention has been paid to the design and synthesis of other pentagon-based 2D materials from unitary penta-sheets (C, Si, …) to binary penta-sheets (CN_{2}, CB_{2}, BN_{2}, PdSe_{2},…), and to ternary penta-sheet (BCN, ZnCP), exhibiting tunable properties changing from semiconducting to metallic, to halfmetallic and to topologically insulating, and from negative Poisson’s ratio to piezoelectricity, to ferroelectricity, and to second harmonic generation susceptibility. This database provides a brief summary on such structures and research articles published so far.

[1] S.H. Zhang, et al., *PNAS *112, 2372 (2015)

[2] T. Bally, S. Chai, M. Neuenschwander, *et al*., *J. Am. Chem. Soc.119, *1869-1875 (1997)

[3] A.de Meijere, P. R. Schreiner, FM Schüngel, *et al*., *Chem. Commun.* 2189–2190 (1999)

[4] K.Y. Chernichenko, V. V. Sumerin, R.V. Shpanchenko, *et al.,* *Angew. Chem.* 118, 7527-7530 (2006)

[5] X. Zeng, H. Li, H.Sun, *et al*., *Angew. Chem. Int. Ed*. 54, 1327 – 1330 (2015)

[6] A. Velian and C. C. Cummins, *Science *348, 1001-1004 (2015)