POLY.X(1)

💖 poly.x, poly-<num>d.x — bestie, we're computing polytope data 💖

okay so this is a page from the User Commands manual, and it's all about poly.x and its little sibling programs poly-<num>d.x. no cap, if you've ever wanted to know everything about a polytope, this is the vibe. ✨

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✨ NAME ✨

poly.x, poly-<num>d.x — computes data of a polytope. that's the whole job, she's a data girlie 🎀

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🌸 SYNOPSIS 🌸

poly.x [-<Option-string>] [in-file [out-file]]

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🦋 DESCRIPTION 🦋

She computes data of a polytope P. literally that's it, that's her whole personality. 💅

The poly-<num>d.x variant programs, where <num> is one of 4, 5, 6 and 11, work in different dimensions. and poly.x itself? she defaults to dimension 6. default queen 👑

💜 Options (concatenate any number of them into <Option-string>) 💜

yes bestie, you smash them all together into one string. go feral.

• h — print this information (hi, that's the help text, she's self-aware)
• f — use as filter
• g — general output. for P reflexive: numbers of (dual) points/vertices, Hodge numbers. and if P is not reflexive: numbers of points, vertices, equations
• p — points of P
• v — vertices of P
• e — equations of P/vertices of P-dual
• m — pairing matrix between vertices and equations
• d — points of P-dual (only if P reflexive, no exceptions 🚨)
• a — all of the above except h, f
• l — LG-`Hodge numbers' from single weight input
• r — ignore non-reflexive input
• D — dual polytope as input (ref only)
• n — do not complete polytope or calculate Hodge numbers
• i — incidence information
• s — check for span property (only if P from CWS)
• I — check for IP property
• S — number of symmetries
• T — upper triangular form
• N — normal form
• t — traced normal form computation
• V — IP simplices among vertices of P*
• P — IP simplices among points of P* (with 1<=codim<=# when # is set)
• Z — lattice quotients for IP simplices
• # — #=1,2,3 fibers spanned by IP simplices with codim<=#
• ## — ##=11,22,33,(12,23): all (fibered) fibers with specified codim(s). when combined: ### = (##)#
• A — affine normal form
• B — Barycenter and lattice volume [# ... points at deg #]
• F — print all facets
• G — Gorenstein: divisible by I>1
• L — like 'l' with Hodge data for twisted sectors
• U — simplicial facets in N-lattice
• U1 — Fano (simplicial and unimodular facets in N-lattice)
• U5 — 5d fano from reflexive 4d projections (M lattice)
• C1 — conifold CY (unimodular or square 2-faces)
• C2 — conifold FANO (divisible by 2 & basic 2 faces)
• E — symmetries related to Einstein-Kaehler Metrics

🍓 Input 🍓

degrees and weights d1 w11 w12 ... d2 w21 w22 ... or d np or np d

(where d=Dimension, np=#[points])

...and then (after a newline) np*d coordinates. yes you have to feed her the coordinates, she's not a mind reader 💀

🌈 Output 🌈

as specified by options. you asked for it, you got it, slay.

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👑 SEE ALSO 👑

a complete manual is available here: http://arxiv.org/abs/1205.4147 — go read it, it's giving academic ✨

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and that's the whole page bestie!! this is from poly.x (palp) 2.1, dated May 2012 — yes she's an elder but she still ate and left no crumbs. mwah 💋🫶