A Penrose tiling never repeats and has fivefold symmetry, which is why it looks so odd on a 3D-printed ornament. You can generate one in about 40 lines of Python with manifold3d. The trick is Robinson triangle subdivision: start with a wheel of 10 triangles and split each one by the golden ratio, again and again.

import math, numpy as np phi = (1 + 5 ** .5) / 2 def subdivide(tris): out = [] for col, A, B, C in tris: # points are complex numbers  if col == 0: # thin (red) triangle  P = A + (B - A) / phi out += [(0, C, P, B), (1, P, C, A)] else: # thick (blue) triangle  Q = B + (A - B) / phi R = B + (C - B) / phi out += [(1, R, C, A), (1, Q, R, B), (0, R, Q, A)] return out Rd = 29.0 tris = [] for i in range(10): B = Rd * 1.3 * np.exp(1j * (2 * i - 1) * math.pi / 10) C = Rd * 1.3 * np.exp(1j * (2 * i + 1) * math.pi / 10) if i % 2 == 0: B, C = C, B tris.append((0, 0j, B, C)) for _ in range(4): tris = subdivide(tris)

After 4 rounds you have 890 triangles. The rhombus edges of the tiling are the A-B and C-A sides of every triangle, so draw those and skip the rest. Deduplicate shared edges, then thicken each one into a thin rectangle with CrossSection:

from manifold3d import Manifold, CrossSection import manifold3d as M3 def seg(a, b, w=0.62): d = b - a sq = CrossSection.square([abs(d), 2 * w], True) return sq.rotate(math.degrees(math.atan2(d.imag, d.real))).translate( [(a.real + b.real) / 2, (a.imag + b.imag) / 2]) edges, segs = set(), [] for col, A, B, C in tris: for p, q in ((A, B), (C, A)): k = tuple(sorted(((round(p.real, 3), round(p.imag, 3)), (round(q.real, 3), round(q.imag, 3))))) if k not in edges: edges.add(k) segs.append(seg(p, q)) disc = CrossSection.circle(Rd, 128) pat = CrossSection.batch_boolean(segs, M3.OpType.Add) ^ disc rim = disc - CrossSection.circle(Rd - 2.0, 128) part = (pat + rim).extrude(2.4) # flat 2.4 mm plate, prints in about 15 minutes

Gotchas

  • Round the endpoints before hashing edges, or floating-point noise leaves duplicate edges and slivers.
  • Use 4 subdivisions for a 58 mm disc. At 5 the tiles are 3 mm wide and clog a 0.4 mm nozzle.
  • Check CrossSection.decompose() for loose islands before you extrude. Keep only the largest piece so nothing floats.
  • Line width of 1.2 mm (3 nozzle widths) prints cleanly with no supports.

If you would rather skip the code, the finished ornament is on Cults3D for $1.27.