☂️[Feature] More operations!

[tesseralis]

Umbrella issue for new operations I want to add, and new polyhedra to apply current operations to.

New operations

~~Coxeter snub / Semi-snub~~

The coxeter snub is an alternative definition of snub equivalent to truncation and alternation (keeping every other vertex). It operates on:

• octahedron -> icosahedron
• cuboctahedron -> snub cube
• icosidodecahedron -> snub dodecahedron

Alternation

• bevelled -> snub
• P(2n) -> An

~~Double / Halve~~

This is the lateral expansion of prisms and pyramids - turns a pyramid to a cupola and doubles the base type of prisms and antiprisms. Also works for augmented cupolae, bipyramids, etc.

name ideas:

• inflate, grow, enlarge, dilate, embiggen
• shrink, minify, ??

~~Increment/decrement~~

Increment adds a size to prisms, pyramids, and cupolae. e.g. triangular pyramid -> square pyramid. Decrement does the opposite.

Fold/unfold

Special one-off operations that create Elementary Johnson solids like the sphenocorona from other solids. Examples include:

• Sphenocorona - created by "folding" one of the square faces of an elongated pentagonal bipyramid
• Hebespenomegacorona - unfold an edge of the icosahedron
• Sphenomegacorona - folding the middle square face of the hebesphenomegacorona (the other way than would result in an icosahedron)
• Disphenocingulum - created by taking a [hexagonal antiprism], treating its hexagonal bases as six triangles, and transforming two opposite triangles on each base from triangles to squares, pulling them out
• Bilunabirotunda - take two opposite vertices of a cuboctahedron and "pinch" them, spreading them out to make the square faces pentagons
• Triangular hebesphenorotunda take an icosidodecahedron and cut it across its pentagonal faces, then normalize them.
  • Alternately, push up the faces of a triaugmented hexagonal prism

Existing operations, new polyhedra

~~Double/halve more polyhedra~~

• ~~augmented prisms~~
• ~~gyroelongated capstones~~

Rectify pyramids into antiprisms + semisnub

• digonal antiprism (tetrahedron) -> snub disphenoid
• square antiprism -> snub square antiprism

Dual of more polyhedra

• ~~Prisms <-> bipyramids~~
• Pyramids <-> pyramids

Increment/Decrement more polyhedra

• cupolae
• augmented prisms

~~Truncation of augmented solids~~

~~e.g. augmented dodecahedron -> augmented truncated dodecahedron~~

Resolved with: #168

~~Rectifying rectified solids~~

Rectifies and normalizes rectified polyhedra:

• octahedron (tetratetrahedron) -> cuboctahedron (rhombitetratetrahedron)
  • already possible
• cuboctahedron -> rhombicuboctahedron
• icosidodecahedron -> rhombicosidodecahedron

This can be considered the equivalent operation of the Coxeter snub/semi-snub.

Truncated -> Rectified

There should be an operation that takes a truncated polyhedron and "continues" the truncation, turning it to the properly rectified version. The "sharpen" operation will similarly need to be updated/split to allow sharpening a rectified polyhedron into a truncated solid or a platonic solid.

~~Expand prisms -> elongated orthobicupolae~~

• triangular prism -> elongated triangular orthobicupola
• cube -> rhobmicuboctahedron
• pentagonal prism -> elongated pentagonal orthobicupola

~~Twist on snub antiprisms~~

Issue: #32

The snub antiprisms can be twisted to form gyrobicupolae:

• Snub disphenoid -> gyrobifastigium
• snub triangular antiprism (icosahedron) -> triangular gyrobicupola (cuboctahedron)
  • (already implemented)
• snub square antiprism -> square gyrobicupola

Misc. individual operations

• Shorten the elongated square orthobicupola into an elongated square bipyramid
• (gyro-)elongate a snub square antiprism into a snub cube

And more!

Have you found some cool relationship between polyhedra? Comment here and I'll add it to the list :)