Elvikar

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Elvikar is an origami crease-pattern 🔢 designer that does two things a printed
diagram 📊 cannot: it folds your pattern 🔢, and it tells you when your pattern cannot
be folded.

DRAW THE PATTERN 🔢
Drag ✋ from point to point to lay a crease. Tap 👆 it to make it a mountain, then a
valley. Bearings snap to 15 degrees until you turn that off. The sheet is real
paper: it has a width, a height, a thickness and a grain direction, and a crease
has to live on it.

FOLD IT, NOT A PICTURE OF IT
Pull the fold handle and the folded form moves under your finger, frame by
frame, from the flat sheet to fully collapsed. There is no Calculate button in
this app 📱. The folded form is computed from the geometry with one degree of
freedom and no iteration, so it is exact at every position of the handle —
mountain and valley are read off the sign of the dihedral angle rather than
copied from a table 📋.

IT TELLS YOU WHICH VERTEX IS WRONG ❌
Maekawa's theorem, Kawasaki's theorem and the Big-Little-Big lemma are evaluated
at every interior vertex, live, every time ⏱️ you move a crease. When a pattern 🔢
stops folding you get the vertex number 🔢, the theorem that broke, and the
numbers 🔢: the mountain and valley counts, both alternating angle sums, the sector
that is too small. Never the word "invalid".

FOUR TESSELLATION FAMILIES, PARAMETRIC
Miura, tapered Miura, arched Miura and herringbone, with live sliders for sector
angle, column pitch, row pitch, columns, rows, taper and arch. Both canvases
update as you drag ✋.

MEASURED, NOT QUOTED
Compression, footprint, height, total 💯 crease length, mountain and valley counts,
degrees of freedom per vertex, layer-stack height — and Poisson's ratio measured
from the footprint's own response across the fold range instead of quoted per
family.

PAPER THAT BEHAVES LIKE PAPER
Pick a stock — kami, tant, copy paper, foil-backed, washi — with its real
thickness, and the app 📱 multiplies it by the deepest layer count. When the stack
passes about 3 mm it says the last folds will not close, because geometry alone
will happily tell you a model closes when the paper will not.

PRINT AND PAIR
Export 📤 the crease sheet at 1:1 to your gallery 🖼️, mountains solid and valleys
dashed in the print convention. Fold it in paper, photograph it, and the photo 📸
pairs with the pattern 🔢 it came from.

HOW IT'S COMPUTED
A Glossary screen ships the actual derivations — both theorems worked on one
vertex, the translation-surface fold with its single constraint, the
spherical-polygon vertex solve — and states plainly what is not computed: layer
ordering. Deciding whether a whole sheet passes through itself is NP-hard, which
is exactly why ❓ this app 📱 checks vertices instead of claiming a verdict on the
sheet.

WHAT IT IS NOT
Not a library 📚 of downloaded diagrams. Not a step-by-step tutorial app 📱.

Fully offline 📴. No account, no ads, no analytics 📊, no tracking. Nothing you draw
leaves the device 📱.