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Cube and Pyramid Combination Demo

Cube and Pyramid Combination Demo
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2020-03-10 03:12
PolygonSolid GeometryGeometric Construction
This example demonstrates the combination of a cube and a pyramid, showcasing 3D geometric shapes and constructions. It involves core concepts like solid geometry, polygons, geometric construction, and spatial visualization. The construction uses GeoGebra commands such as Point, Cube, Pyramid, along with precise definitions of vertices, faces, and edges. Suitable for high school students learning 3D geometry and spatial reasoning, or for math clubs' demonstrations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH_1, arestaAD, arestaAB_1, arestaBC, arestaCD, arestaAE_1, arestaDH, arestaEH_1, arestaEF_1, E, arestaBF_1, arestaFG_1, arestaCG_1, arestaGH_1, F, G, H, faceABCD, faceADHE, faceABFE_1, faceBCGF
  5. Point(zAxis) → I
  6. Pyramid(E, F, G, H, I) → b, faceEFGH, arestaEI, arestaFI, arestaGI, arestaHI, faceEFI, faceFGI, faceGHI, faceEHI, arestaEF_2, arestaFG_2, arestaGH_2, arestaEH_2
  7. Pyramid(E, F, B, A, J) → c, faceABFE, arestaEJ, arestaFJ, arestaBJ, arestaAJ, faceEFJ, faceBFJ, faceABJ, faceAEJ, arestaEF, arestaBF_2, arestaAB, arestaAE_2
  8. Point(yAxis) → K
  9. Pyramid(H, E, A, K, L) → d, faceAEHK, arestaHL, arestaEL, arestaAL, arestaKL, faceEHL, faceAEL, faceAKL, faceHKL, arestaEH, arestaAE, arestaAK, arestaHK_1
  10. Pyramid(H, K, C, G, M) → e, faceCGHK, arestaHM, arestaKM, arestaCM, arestaGM, faceHKM, faceCKM, faceCGM, faceGHM, arestaHK, arestaCK, arestaCG, arestaGH
  11. Point(xAxis) → N
  12. Pyramid(F, B, N, G, O) → f, faceBFGN, arestaFO, arestaBO, arestaNO, arestaGO, faceBFO, faceBNO, faceGNO, faceFGO, arestaBF, arestaBN, arestaGN, arestaFG

AI Drawing Prompt Reference

Draw a combination of a cube and a pyramid, where the cube is defined by three points and the pyramid by four points including part of the cube's face. Place one pyramid on one face of the cube, another on another face, a third on one edge, and a fourth on one corner, showcasing 3D geometric shapes and constructions for spatial reasoning.
The prompt above was compiled from the original drawing commands and is for reference only.