Chemical substance identity of benzene, until the correct structure was described by Friedrich August Kekulé. Likewise, the idea of stereoisomerism – that atoms have rigid three-dimensional structure and can thus form isomers that differ only in their three-dimensional arrangement – was another crucial step in understanding the concept of distinct chemical substances. For example, tartaric acid has three distinct isomers, a pair of diastereomers with one diastereomer forming two enantiomers. An element is a chemical substance made up of a particular kind of atom and hence cannot be broken down or transformed by a chemical reaction into a different element, though it
Magic cube classes MAY be pandiagonal magic. Gardner also called this (Langman’s pandiagonal) a ‘perfect’ cube, presumably not realizing it was a higher class then Myer’s cube. See previous note re Boyer and Trump. <br>The smallest normal pandiagonal magic cube is order 7. See Pandiagonal magic cube.<br>Minimum correct summations required = 9"m" + 4. All pan-"r"-agonals sum correctly for "r" = 1 and 2. ALL 3"m" planar arrays must be pandiagonal magic squares. In addition, ALL pantriagonals must sum correctly. These two conditions combine to provide a total of 9m pandiagonal magic squares. <br>The smallest normal perfect magic cube is order 8. See