Cube Dissected into Three Yangma

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2017-03-01 06:18

This example demonstrates the dissection of a cube into three yangma. It involves core mathematical concepts such as solid geometry, polygons, transformations, and spatial relationships. The construction utilizes GeoGebra commands and objects like Intersect, Point, Cube, and Pyramid as outlined in the summary. It is suitable for high school and above students to learn complex geometric dissections and spatial geometry properties, ideal for teaching solid geometry and geometric constructions.

GeoGebra Commands & Parameters

Intersect(zAxis, xOyPlane) → A
Point(xAxis) → B
Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
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
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
Pyramid(G, H, D, C, E) → c, faceCDHG, edgeEG_1, edgeEH, edgeDE, edgeCE_2, faceEGH, faceDEH, faceCDE, faceCEG_1, edgeGH, edgeDH, edgeCD, edgeCG_2
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 yangma. Start by drawing the coordinate axes and the origin, then construct the cube using these points. Next, use the vertices of the cube as the base points to construct three yangma, ensuring their bases are coplanar with the cube's base and their peaks are at the cube's top vertex. Finally, make sure the sides of the yangma intersect with the cube's sides to form the correct geometric relationships.

The prompt above was compiled from the original drawing commands and is for reference only.