<P> The internal angles of a flat regular hexagon are 120 °, while the preferred angle between successive bonds in a carbon chain is about 109.5 °, the tetrahedral angle . Therefore, the cyclohexane ring tends to assume certain non-planar (warped) conformations, which have all angles closer to 109.5 ° and therefore a lower strain energy than the flat hexagonal shape . The most important shapes are called chair, half - chair, boat, and twist - boat . The molecule can easily switch between these conformations, and only two of them--chair and twist - boat--can be isolated in pure form . </P> <P> Cyclohexane conformations have been extensively studied in organic chemistry because they are the classical example of conformational isomerism and have noticeable influence on the physical and chemical properties of cyclohexane . </P> <P> In 1890, Hermann Sachse, a 28 - year - old assistant in Berlin, published instructions for folding a piece of paper to represent two forms of cyclohexane he called symmetrical and unsymmetrical (what we would now call chair and boat). He clearly understood that these forms had two positions for the hydrogen atoms (again, to use modern terminology, axial and equatorial), that two chairs would probably interconvert, and even how certain substituents might favor one of the chair forms . Because he expressed all this in mathematical language, few chemists of the time understood his arguments . He had several attempts at publishing these ideas, but none succeeded in capturing the imagination of chemists . His death in 1893 at the age of 31 meant his ideas sank into obscurity . It was only in 1918 when Ernst Mohr, based on the molecular structure of diamond that had recently been solved using the then very new technique of x-ray crystallography, was able to successfully argue that Sachse's chair was the pivotal motif . Derek Barton and Odd Hassel shared the 1969 Nobel Prize for work on the conformations of cyclohexane and various other molecules . </P> <Table> <Tr> <Td> </Td> <Td> This section needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (May 2014) (Learn how and when to remove this template message) </Td> </Tr> </Table>

Using a suitable diagram explain the relative energies of various conformations of (5) cyclohexane