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BeakUnit: Skeletal Cuboctahedron (6 units)

BeakUnit: Skeletal Cuboctahedron (6 units)
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2020-07-17 00:32
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections Action Modular Origami
① This example demonstrates an animated rotating model of a skeletal cuboctahedron folded from six beak units, showcasing the spatial structure of a polyhedral framework. ② Core mathematical concepts include solid geometry of Archimedean solids—specifically the cuboctahedron with 8 triangular and 6 square faces—and the geometric connections between origami units. ③ Construction highlights: based on the construction summary, GeoGebra commands such as Intersect, Point, Cube, Midpoint, Polygon, Line, Rotate, Plane, Mirror, Translate, Angle, and OrthogonalLine are used to build a cube and its faces, edges, midpoints, then generate the skeletal polyhedron via rotations and translations. ④ Suitable for high school or early college students for spatial visualization training in solid geometry, and as a visual aid for origami mathematics and polyhedra education.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Midpoint(E, F) → I
  6. Midpoint(F, G) → J
  7. Midpoint(F, B) → K
  8. Polygon(I, K, J) → poly1, j, i, k
  9. Midpoint(A, G) → OO
  10. Polygon(K, I, 4, faceABFE) → poly2, f, g, h, l, L, M
  11. Line(OO, F) → m
  12. Rotate(poly2, 120°, m) → poly2'
  13. Line(N, I) → n
  14. Plane(I, N, M) → b
  15. Point(n) → O
  16. Rotate(O, (-rot), N, b) → O'
  17. Polygon(O', OO, K) → poly3, p, q, r
  18. Plane(L, K, OO) → c
  19. Mirror(poly3, c) → poly3'
  20. Mirror(poly3, b) → poly3'_1
  21. Mirror(poly3', b) → poly3''
  22. Midpoint(B, C) → P
  23. Plane(OO, J, P) → d
  24. Translate({poly3, poly3', poly3'', poly3'_1}, Vector[OO, OO]) → polyList1
  25. Mirror(polyList1, d) → polyList1'
  26. Translate({polyList1, polyList1'}, Vector[OO, OO]) → polyList11
  27. Angle(O, K, OO) → α
  28. OrthogonalLine(N, xOyPlane) → s
  29. Rotate(polyList11, β, s) → polyList11'_2
  30. Rotate(Rotate[polyList11, 240°, m], β, s) → polyList11'_1
  31. Rotate(Rotate[polyList11, 120°, m], β, s) → polyList11'

AI Drawing Prompt Reference

Draw an animated rotating model of a skeletal cuboctahedron folded from six beak units, showcasing its spatial structure. The model should include a cube with its faces, edges, and midpoints, then generate the skeletal polyhedron via rotations and reflections to highlight geometric connections. The model should rotate around a central axis to observe its solid geometry structure.
The prompt above was compiled from the original drawing commands and is for reference only.