Final answer:
In mathematics, the three primary isometries are translation, rotation, and reflection, with no common slang terms. These terms describe different ways a geometrical figure can be manipulated in space. In organic chemistry, primary, secondary, and tertiary refer to the number of carbon attachments on an alkyl group, not to isometries.
Step-by-step explanation:
The three primary isometries are translation, rotation, and reflection. In a translation, all points of a figure move the same distance in the same direction. In a rotation, all points of the figure rotate around a fixed point at a certain angle. A reflection is a flip over a line where the image is a mirror image of the preimage. Slang terms for these isometries are not commonly used in mathematics and are not essential for understanding the concepts.
When discussing organic chemistry nomenclature, alkyl groups can be categorized as primary (p), secondary (sec or s), or tertiary (t). These terms refer to the number of carbon atoms attached to the carbon atom of interest. Specifically, primary alkyl groups have one carbon group attached to the alpha carbon, secondary have two, and tertiary have three. These designations are often used in common names of organic compounds, such as isopropyl in place of sec-propyl. However, this is unrelated to the mathematical concept of isometries.