Polyhedra in OpenSCAD

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Conway operators

Conway formula either stored with the polyhedron data or entered manually allow an range of operators identified by a single lower-case (for operators) or upper-case (for primitives and decorative transforms). Each can be parameterised, either with a single number "k5" or full parameters in parentheses "k(fn=5,h=0.5)".
Conway code OpenSCAD function Parameters Canonicalisation Description
a ambo truncation to the edge midpoint, so each N-vetex becomes an N-face, each M-face replaced by an inscribed M-face
b bevel
c chamfer r=0.333 every edge is replaced by a hexagon
d dual exchange vertices and faces - every vertex bceomes a face, the centroid of every face a vertex
e expand h=0.5
f
g gyro h=0.2,r=0.3333 each N-face is divided into N pentagons composed of a vertex, two edge points and the centroid
h
i inset_kis fn=[],r=0.5,h=0.1 like kis but inset from the edge by ratio r - Conway's operator i is dk
j join
k kis fn=[],h=0.1,regular=false each N-face is divided into N triangles which extend to the face centroid moved normal to the face by h
l
m meta h=0.1 each N-face is divided into 2N triangles
n inset r=0.3, h=-0.1 inset face
o ortho h=0.2 each N-face becomes N quadrilaterals
p propellor r=0.333 a face rotation that creates N quadrilaterals at an N-vertex
q quinta not yet implemented
r reflect mirror image vertices for chiral forms
s snub h=0.5 'expand and twist' - each vertex replaced by a face and each edge creates 2 triangles
t trunc fn=[],r=0.25 truncate selected vertices - r determines the point of truncation. Each N-face becomes an N-face, each N-vertex an N-face
u pt tri-triangulate pentagonal faces ? whats this for?
v tt quad triangulate triangular faces
w whirl h=0.2,r=0.3333 each edge becomes 2 hexagons with the face reduced - also called hexpropello (Dave Mccooey)
x qt bi-triangulate quadrilateral faces
y pyra h=0.1 added by KW - like inset-kis
z
G orient orient the faces - needed for some wrl derived solids
L openface Leonardo's open face form
F place place on largest face
M modulate modulate the vertex positions with spherical function fmod(r,theta,phi)
N canon n=10 George Hart's full canonicalisation
K plane n=10 George Hart's simple canonicalisation
S rcc n=1 apply the Catmull-Clark smoothing operation recursively to a depth of n
R random o=0.1 perturb each vertice by a random vector scaled by parameter o
X skew alpha=0,beta=0 skew vertices by alpha in Z-X plane and beta in Z-Y plane (i think)
V invert invert vertices
Z Z Use the polyhedron defined by coordinates
T T Tetrahedron
C C Cube
O O Octahedron
D D Dodecahedron
I I Icosahedron
A A n,h=1 Antiprism
Y Y n,h=1 Pyramid
P P n,h=1 Prism