VII. On the partitions of the R -pyramid, being the first class of R -gonous X -edra

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Abstract
I. As the partitions of an r -gon are made by drawing diagonals , so the partitions of an r -ace are made by drawing diapeds , each a line in two faces non-contiguous about the r -ace. A partitioned r -ace standing on a partitioned r -gon is a partitioned pyramid of r -gonal base and vertex. I am about to determine the number of such partitions of this r -pyramid, that can be made with K diapeds and k diagonals, so that no two partitions shall be syntypous; i. e . one the repetition or the reflected image o f the other. I have proved in a memoir “On Autopolar Polyedra” in the Transactions of the Royal Society for 1857, that the problem of the polyedra reduces itself to the determination of the x -edra generable from the r -pyramid. Such an x -edron is r -gonous.

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