كتل (root ktl)

al-Khalīl (d. c. 170/786), Kitāb al-ʿAyn, as transmitted by al-Layth: a two-letter word “turns in two ways”, a three-letter word “in six ways” (masdūsa), four letters in 24, five in 120; “its used forms are written down and its unused ones dropped” (line 975 ↗). The dictionary is built on this: each chapter takes a set of letters and names which orders are used (mustaʿmal) and which unused (muhmal). The ring shows that verdict, from the chapter heading as edited (documented in the text; how much of the book is al-Khalīl's own is disputed).

A reported total. al-Suyūṭī transmits, from Ḥamza al-Iṣfahānī, that al-Khalīl put the possible forms, used and unused, of two to five letters at 12,305,412 (al-Muzhir, line 1347 ↗). It is reported, not found in the ʿAyn. It equals exactly the arrangements of 2 to 5 different letters out of 28 (756 + 19,656 + 491,400 + 11,793,600); the breakdown printed beside it is corrupt, and al-Zubaydī's count, given next, differs (6,659,400).

Ibn Jinnī (d. 392/1002), al-Khaṣāʾiṣ, names the greater derivation (al-ishtiqāq al-akbar): bind a three-letter root and its six orders to one meaning, and bring stray members back “by the subtlety of the craft and interpretation” (line 7536 ↗). He says himself that it does not hold for every root (line 167 ↗; line 7603 ↗).

Ibn Fāris (d. 395/1004) gives each root its own aṣl and treats a rearranged word as maqlūb, “turned round”, and so not a root of its own: “j-b-dh is not a root, because it is a single word, turned round” (Maqāyīs, line 6147 ↗). The ring sets his aṣl for each order side by side; whether they meet is the question.

Neighbours on the ring differ by one swap of two letters.

The critique. A source quoted by al-Suyūṭī calls the greater derivation Ibn Jinnī's innovation, “not relied on in the language” (al-Muzhir, line 6159 ↗).

The other axis. The root's letters also go into patterns that keep their order and change the frame: the patterns (awzān) and the verb Forms I–X.

Attested here means found in our digital texts (Ibn Fāris, Lisān al-ʿArab, Lane, the Quranic Arabic Corpus), with w and y kept apart and hamza spellings merged; it is our data, not a classical verdict. English beside the Arabic is AI translation. Sources and grades: docs/research/root-permutations.md.