add polar_zonohedra

src/polyhedra/geom_polar_zonohedra.scad

@@ -0,0 +1,33 @@
+use <../util/sum.scad>;
+use <../util/flat.scad>;
+
+function vertex(i, j, n, theta) = 
+    i > j ? [0, 0, 0] : 
+	        sum([
+			    for(k = [i:j]) 
+				let(
+					cosa = cos(theta),
+					a_i_n = 360 * k / n
+				)
+				[cosa * cos(a_i_n), cosa * sin(a_i_n), sin(theta)]
+			]);
+
+function rhombi(i, j, n, theta) = [
+	vertex(i, j, n, theta),
+	vertex(i + 1, j, n, theta),
+    vertex(i + 1, -1 + j, n, theta),
+	vertex(i, -1 + j, n, theta)
+];
+
+function geom_polar_zonohedra(n, theta = 35.5) = 
+    let(
+        points = flat([
+            for(i = [0:n - 1], j = [i + 1:n + i - 1])
+                rhombi(i, j, n, theta)
+        ]),
+        faces = [
+            for(i = [0:len(points) / 4 - 1]) 
+            [for(j = [0:3]) i * 4 + j]
+        ]
+    )
+    [points, faces];

src/polyhedra/polar_zonohedra.scad

@@ -0,0 +1,17 @@
+// http://archive.bridgesmathart.org/2021/bridges2021-7.pdf
+
+// use <util/sum.scad>;
+// use <util/flat.scad>;
+// use <polyhedra/polar_zonohedra.scad>;
+
+// for(n = [3:8]) {
+//     translate([0.5 * n * (n - 3), 0, 0])
+//         polar_zonohedra(n);
+// }
+
+use <geom_polar_zonohedra.scad>;
+
+module polar_zonohedra(n, theta = 35.5) {
+    points_faces = geom_polar_zonohedra(n, theta);
+	polyhedron(points_faces[0], points_faces[1]);
+}