Chemical substance In organic chemistry, there can be more than one chemical compound with the same composition and molecular weight. Generally, these are called isomers. Isomers usually have substantially different chemical properties, and often may be isolated without spontaneously interconverting. A common example is glucose vs. fructose. The former is an aldehyde, the latter is a ketone. Their interconversion requires either enzymatic or acid-base catalysis. However, tautomers are an exception: the isomerization occurs spontaneously in ordinary conditions, such that a pure substance cannot be isolated into its tautomers, even if these can be identified spectroscopically or even isolated in special conditions. A
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