for the end-words of the first stanza. Each successive stanza takes its pattern based upon a bottom-up pairing of the lines of the preceding stanza (i.e., last and first, then second-from-last and second, then third-from-last and third). Given that the pattern for the first stanza is 123456, this produces 615243 in the second stanza, numerical series which corresponds, as Paolo Canettieri has shown, to the way in which the points on the dice are arranged. This genetic hypothesis is supported by the fact that Arnaut Daniel was a strong dice player and various images related to this game are present in his poetic texts. Another way of visualising the pattern of line-ending words for each stanza is by the procedure known as retrogradatio cruciata, which may be rendered as "backward crossing". The second stanza can be seen to have been formed from three sets of pairs (6–1, 5–2, 4–3), or two triads (1–2–3, 4–5–6). The 1–2–3 triad appears in its original order, but the 4–5–6 triad is reversed and superimposed upon it. The pattern of the line-ending words in a sestina is represented both numerically and alphabetically in the following table: The sixth stanza is followed by a tercet that is known variably by the French term envoi, the Occitan term tornada, or, with reference to its size in relation to the preceding stanzas, a "half-stanza". It consists of three lines that include all six of the line-ending words of the preceding stanzas. This should take the pattern of 2–5, 4–3, 6–1 (numbers relative to the first stanza); the first end-word of each pair can occur anywhere in the line, while the second must end the line. However, the end-word order of the envoi is no longer strictly enforced. The sestina has been subject to some variations, with changes being made to both the size and number of stanzas, and also to individual line length. A "double sestina" is the name given to either: two sets of six six-line stanzas, with a three-line envoy (for a total of 75 lines), or twelve twelve-line stanzas, with a six-line envoy (for a total of 150 lines). Examples of either variation are rare; "Ye Goatherd Gods" by Philip Sidney is a notable example of the former variation, while "The Complaint of Lisa" by Algernon Charles Swinburne is a notable example of the latter variation. In the former variation, the original pattern of line-ending