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Cube with Diagonal Cupolaic Blends

Cube with Diagonal Cupolaic Blends
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2015-12-31 17:00
PolygonSolid GeometryTransformationGeometric Construction
This example demonstrates a three‑dimensional model of a cube augmented with diagonal cupolaic blends. It covers core concepts in solid geometry, polyhedron construction, spatial transformations, and symmetry. The construction employs GeoGebra commands such as Cube, Vertex, OrthogonalLine, IntersectConic, Intersect, Rotate, and Polygon to create vertices, edges, faces, and the blended structure via rotations and intersections. It is suitable for high‑school solid geometry lessons, university geometric modeling courses, and advanced GeoGebra construction practice.

GeoGebra Commands & Parameters

  1. Cube(C, B, A) → a, D, A3, A6, krawędźCD, krawędźBC, krawędźAB, krawędźAD, krawędźCE, krawędźDH, krawędźEH, krawędźEF, E, krawędźBF, krawędźFG, krawędźAG, krawędźGH, F, G, H, A1, A5, A4, A2
  2. Vertex(A1, 1) → B1
  3. Vertex(A1, 2) → C1
  4. Vertex(A1, 3) → D1
  5. Vertex(A1, 4) → E1
  6. OrthogonalLine((B1 + D1) / 2, Plane[A1]) → F1
  7. IntersectConic(Sphere[C1, 2], Sphere[D1, 2]) → G1
  8. IntersectConic(Sphere[C1, 2], Sphere[B1, (2 * sqrt(2))]) → H1
  9. Intersect
  10. Intersect(G1, H1, 2) → I1
  11. Rotate(I1, 90°, $F1) → J1
  12. Rotate(J1, 90°, $F1) → K1
  13. Rotate(K1, 90°, $F1) → L1
  14. Polygon(B1, E1, K1) → N1, O1, P1, Q1
  15. Polygon(B1, C1, L1) → R1, S1, T1, U1
  16. Polygon(C1, D1, I1) → V1, W1, X1, Y1
  17. Polygon(B1, K1, M1) → AD1, AE1, AF1, AG1
  18. Polygon(B1, L1, M1) → AH1, AI1, AJ1, AK1
  19. Polygon(C1, M1, L1) → AL1, AM1, AN1, AO1
  20. Polygon(C1, M1, I1) → AP1, AQ1, AR1, AS1
  21. Polygon(D1, M1, I1) → AT1, AU1, AV1, AW1
  22. Polygon(D1, M1, J1) → AX1, AY1, AZ1, BA1
  23. Polygon(E1, M1, J1) → BB1, BC1, BD1, BE1
  24. Polygon(E1, M1, K1) → BF1, BG1, BH1, BI1
  25. Vertex(A2, 1) → B2
  26. Vertex(A2, 2) → C2
  27. Vertex(A2, 3) → D2
  28. Vertex(A2, 4) → E2
  29. OrthogonalLine((B2 + D2) / 2, Plane[A2]) → F2
  30. IntersectConic(Sphere[C2, 2], Sphere[D2, 2]) → G2
  31. IntersectConic(Sphere[C2, 2], Sphere[B2, (2 * sqrt(2))]) → H2
  32. Intersect
  33. Intersect(G2, H2, 2) → I2
  34. Rotate(I2, 90°, $F2) → J2
  35. Rotate(J2, 90°, $F2) → K2
  36. Rotate(K2, 90°, $F2) → L2
  37. Vertex(A3, 1) → B3
  38. Vertex(A3, 2) → C3
  39. Vertex(A3, 3) → D3
  40. Vertex(A3, 4) → E3
  41. OrthogonalLine((B3 + D3) / 2, Plane[A3]) → F3
  42. IntersectConic(Sphere[C3, 2], Sphere[D3, 2]) → G3
  43. IntersectConic(Sphere[C3, 2], Sphere[B3, (2 * sqrt(2))]) → H3
  44. Intersect
  45. Intersect(G3, H3, 2) → I3
  46. Rotate(I3, 90°, $F3) → J3
  47. Rotate(J3, 90°, $F3) → K3
  48. Rotate(K3, 90°, $F3) → L3
  49. Vertex(A4, 1) → B4
  50. Vertex(A4, 2) → C4
  51. Vertex(A4, 3) → D4
  52. Vertex(A4, 4) → E4
  53. OrthogonalLine((B4 + D4) / 2, Plane[A4]) → F4
  54. IntersectConic(Sphere[C4, 2], Sphere[D4, 2]) → G4
  55. IntersectConic(Sphere[C4, 2], Sphere[B4, (2 * sqrt(2))]) → H4
  56. Intersect
  57. Intersect(G4, H4, 2) → I4
  58. Rotate(I4, 90°, $F4) → J4
  59. Rotate(J4, 90°, $F4) → K4
  60. Rotate(K4, 90°, $F4) → L4
  61. Vertex(A5, 1) → B5
  62. Vertex(A5, 2) → C5
  63. Vertex(A5, 3) → D5
  64. Vertex(A5, 4) → E5
  65. OrthogonalLine((B5 + D5) / 2, Plane[A5]) → F5
  66. IntersectConic(Sphere[C5, 2], Sphere[D5, 2]) → G5
  67. IntersectConic(Sphere[C5, 2], Sphere[B5, (2 * sqrt(2))]) → H5
  68. Intersect
  69. Intersect(G5, H5, 2) → I5
  70. Rotate(I5, 90°, $F5) → J5
  71. Rotate(J5, 90°, $F5) → K5
  72. Rotate(K5, 90°, $F5) → L5
  73. Vertex(A6, 1) → B6
  74. Vertex(A6, 2) → C6
  75. Vertex(A6, 3) → D6
  76. Vertex(A6, 4) → E6
  77. OrthogonalLine((B6 + D6) / 2, Plane[A6]) → F6
  78. IntersectConic(Sphere[C6, 2], Sphere[D6, 2]) → G6
  79. IntersectConic(Sphere[C6, 2], Sphere[B6, (2 * sqrt(2))]) → H6
  80. Intersect
  81. Intersect(G6, H6, 2) → I6
  82. Rotate(I6, 90°, $F6) → J6
  83. Rotate(J6, 90°, $F6) → K6
  84. Rotate(K6, 90°, $F6) → L6
  85. Polygon(B2, E2, K2) → N2, O2, P2, Q2
  86. Polygon(B3, E3, K3) → N3, O3, P3, Q3
  87. Polygon(B4, E4, K4) → N4, O4, P4, Q4
  88. Polygon(B5, E5, K5) → N5, O5, P5, Q5
  89. Polygon(B6, E6, K6) → N6, O6, P6, Q6
  90. Polygon(B2, C2, L2) → R2, S2, T2, U2
  91. Polygon(B3, C3, L3) → R3, S3, T3, U3
  92. Polygon(B4, C4, L4) → R4, S4, T4, U4
  93. Polygon(B5, C5, L5) → R5, S5, T5, U5
  94. Polygon(B6, C6, L6) → R6, S6, T6, U6
  95. Polygon(C2, D2, I2) → V2, W2, X2, Y2
  96. Polygon(C3, D3, I3) → V3, W3, X3, Y3
  97. Polygon(C4, D4, I4) → V4, W4, X4, Y4
  98. Polygon(C5, D5, I5) → V5, W5, X5, Y5
  99. Polygon(C6, D6, I6) → V6, W6, X6, Y6
  100. Polygon(D2, E2, J2) → Z2, AA2, AB2, AC2
  101. Polygon(D3, E3, J3) → Z3, AA3, AB3, AC3
  102. Polygon(D4, E4, J4) → Z4, AA4, AB4, AC4
  103. Polygon(D5, E5, J5) → Z5, AA5, AB5, AC5
  104. Polygon(D6, E6, J6) → Z6, AA6, AB6, AC6
  105. Polygon(D1, E1, J1) → Z1, AA1, AB1, AC1
  106. Polygon(B2, K2, M2) → AD2, AE2, AF2, AG2
  107. Polygon(B3, K3, M3) → AD3, AE3, AF3, AG3
  108. Polygon(B4, K4, M4) → AD4, AE4, AF4, AG4
  109. Polygon(B5, K5, M5) → AD5, AE5, AF5, AG5
  110. Polygon(B6, K6, M6) → AD6, AE6, AF6, AG6
  111. Polygon(B2, L2, M2) → AH2, AI2, AJ2, AK2
  112. Polygon(B3, L3, M3) → AH3, AI3, AJ3, AK3
  113. Polygon(B4, L4, M4) → AH4, AI4, AJ4, AK4
  114. Polygon(B5, L5, M5) → AH5, AI5, AJ5, AK5
  115. Polygon(B6, L6, M6) → AH6, AI6, AJ6, AK6
  116. Polygon(C2, M2, L2) → AL2, AM2, AN2, AO2
  117. Polygon(C3, M3, L3) → AL3, AM3, AN3, AO3
  118. Polygon(C4, M4, L4) → AL4, AM4, AN4, AO4
  119. Polygon(C5, M5, L5) → AL5, AM5, AN5, AO5
  120. Polygon(C6, M6, L6) → AL6, AM6, AN6, AO6
  121. Polygon(C2, M2, I2) → AP2, AQ2, AR2, AS2
  122. Polygon(C3, M3, I3) → AP3, AQ3, AR3, AS3
  123. Polygon(C4, M4, I4) → AP4, AQ4, AR4, AS4
  124. Polygon(C5, M5, I5) → AP5, AQ5, AR5, AS5
  125. Polygon(C6, M6, I6) → AP6, AQ6, AR6, AS6
  126. Polygon(D2, M2, I2) → AT2, AU2, AV2, AW2
  127. Polygon(D3, M3, I3) → AT3, AU3, AV3, AW3
  128. Polygon(D4, M4, I4) → AT4, AU4, AV4, AW4
  129. Polygon(D5, M5, I5) → AT5, AU5, AV5, AW5
  130. Polygon(D6, M6, I6) → AT6, AU6, AV6, AW6
  131. Polygon(D2, M2, J2) → AX2, AY2, AZ2, BA2
  132. Polygon(D3, M3, J3) → AX3, AY3, AZ3, BA3
  133. Polygon(D4, M4, J4) → AX4, AY4, AZ4, BA4
  134. Polygon(D5, M5, J5) → AX5, AY5, AZ5, BA5
  135. Polygon(D6, M6, J6) → AX6, AY6, AZ6, BA6
  136. Polygon(E2, M2, J2) → BB2, BC2, BD2, BE2
  137. Polygon(E3, M3, J3) → BB3, BC3, BD3, BE3
  138. Polygon(E4, M4, J4) → BB4, BC4, BD4, BE4
  139. Polygon(E5, M5, J5) → BB5, BC5, BD5, BE5
  140. Polygon(E6, M6, J6) → BB6, BC6, BD6, BE6
  141. Polygon(E2, M2, K2) → BF2, BG2, BH2, BI2
  142. Polygon(E3, M3, K3) → BF3, BG3, BH3, BI3
  143. Polygon(E4, M4, K4) → BF4, BG4, BH4, BI4
  144. Polygon(E5, M5, K5) → BF5, BG5, BH5, BI5
  145. Polygon(E6, M6, K6) → BF6, BG6, BH6, BI6

AI Drawing Prompt Reference

Draw a cube and add a diagonal cupolaic blend structure on it. First, draw a cube, then create a circle at each vertex of the cube, use the intersection of these circles to construct new vertices, and then rotate these vertices to build the blend structure. Finally, connect these vertices to form new polygons, completing the entire diagonal cupolaic blend structure of the cube.
The prompt above was compiled from the original drawing commands and is for reference only.