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Cube Dissection into Three Square Pyramids

Cube Dissection into Three Square Pyramids
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2017-02-27 13:39
Solid GeometryOptimizationGeometric Construction
This example demonstrates the geometric dissection of a cube into three square pyramids. It involves core mathematical concepts such as solid geometry, polygon division, and volume calculation. The construction is achieved using GeoGebra commands like Intersect, Point, Cube, and Pyramid, highlighting precise spatial geometry manipulation. Suitable for high school students and above to explore spatial geometry decomposition and optimization in teaching.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xOyPlane) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG_1, faceEFGH, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_2, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF_1, edgeFG_1, edgeCG_1, edgeGH_1, F, G, H, faceABCD_1, faceADHE, faceABFE, faceBCGF_1
  5. Pyramid(C, D, A, B, E) → b, faceABCD, edgeCE_1, edgeDE_1, edgeAE, edgeBE_1, faceCDE_1, faceADE, faceABE, faceBCE_1, edgeCD_1, edgeAD, edgeAB, edgeBC_2
  6. Pyramid(G, H, D, C, E) → c, faceCDHG, edgeEG_1, edgeEH, edgeDE, edgeCE_2, faceEGH, faceDEH, faceCDE, faceCEG_1, edgeGH, edgeDH, edgeCD, edgeCG_2
  7. Pyramid(F, G, C, B, E) → d, faceBCGF, edgeEF, edgeEG, edgeCE, edgeBE, faceEFG, faceCEG, faceBCE, faceBEF, edgeFG, edgeCG, edgeBC, edgeBF

AI Drawing Prompt Reference

Draw a cube and dissect it into three identical square pyramids. First, create the three faces of the cube. Then, for each face, draw a square pyramid with its apex at the same vertex as the cube and its base on that face. Ensure the pyramids' bases perfectly match the cube's faces and their sides connect seamlessly with the cube's sides, forming a complete dissection of the cube into three pyramids.
The prompt above was compiled from the original drawing commands and is for reference only.