An optional helper. The facts here are standard geometry, worked out from each shape itself; nothing on this page knows about any puzzle. It runs entirely in your browser, and your notes stay on this device.
Find a shape
Which shape fits? Filter by facts
List the faces around one corner by their number of sides, separated by dots. Use 5/2 for a pentagram. 3^4.5 means 3.3.3.3.5. Starting point and direction don't matter.
Make any prism or antiprism
Step 1 gives an ordinary polygon. A larger step joins every second, third… corner, making a star: 7 sides with step 2 is the heptagram {7/2}. An antiprism with a step between half and two-thirds of the sides is a crossed antiprism.
Pick a shape
This browser can't draw the 3D view, but all the facts are below.
Drag to turn it, or click it and use the arrow keys. Switch face types off to see inside. “One corner” colours just the faces that meet at one corner.
Facts
Lengths are for edges of length 1. Tap + to copy a fact to your notepad.
Notepad
Saved in this browser only. Tap a note's value to put it in the last box you used below.
Nothing noted yet.
Quick coordinate helpers
Digits go in order: degrees, then minutes with three decimals. 14 or 15 digits make a full coordinate; 7 or 8 make one half.
Takes decimal degrees, or degrees minutes seconds (N 45 12 20.7 W 93 54 19.3), and writes them the geocaching way.
Where the facts come from
Each uniform polyhedron here was built from its Wythoff symbol, the classic kaleidoscope construction, and its counts, sizes and symmetry were worked out from the result. Every count, radius and angle was then checked against Wolfram's polyhedron data. The Catalan solids are the exact duals of the Archimedean ones. Prisms and antiprisms are built in your browser as you ask for them.
Names, alternative names and index numbers come from the open-source Antiprism project (MIT licence): U is the uniform polyhedron number (Maeder's index), C Coxeter's, W Wenninger's model number, and K the Kaleido program's. The short names such as “sirsid” are Jonathan Bowers'. George Olshevsky's names for the nonconvex snub polyhedra are also listed in Antiprism, and in a Wikipedia reference desk discussion from 3 May 2012. Only “yog-sothoth” is widely used.
Some sources disagree with each other. Wolfram's data marks the great snub dodecicosidodecahedron (U64) as not chiral, but its own model has no mirror symmetry, and Wikipedia gives it rotation-only symmetry. This page says chiral.