Pyramid Model: Rotating Regular Square Pyramid with Equilateral Triangular Faces

Pyramid Model: Rotating Regular Square Pyramid with Equilateral Triangular Faces
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2016-06-27 10:01
① This example demonstrates a regular square pyramid (pyramid model) in 3D, with rotation around its central axis, showing the square base, equilateral triangular side faces, and auxiliary internal lines. ② Core mathematical concepts include solid geometry of pyramids, regular polygon bases, equilateral triangles, symmetry axes, midpoints and segments, and spatial rotation logic. ③ Construction highlights: using GeoGebra commands Polygon to create the base square, Pyramid to generate the solid, Midpoint to find the center O and edge midpoints, Line and Segment to build the central axis and auxiliary segments; objects include vertices A, B, C, D, V, base poly1, edges a, b, c, d, e, side faces faceABV etc., central axis CentralAxis, and auxiliary points N, K, L, M. ④ Suitable for high school or early college students learning solid geometry, spatial reasoning, and 3D GeoGebra construction, also useful for demonstrating rotational symmetry in mathematical modeling.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Pyramid(poly1, V) → e, faceABV, faceBCV, faceCDV, faceADV, edgeAV, edgeBV, edgeCV, edgeDV
  3. Midpoint(A, D) → N
  4. Midpoint(A, B) → K
  5. Midpoint(B, C) → L
  6. Midpoint(C, D) → M
  7. Line(O, V) → CentralAxis
  8. Segment(L, V) → f
  9. Segment(N, V) → g

AI Drawing Prompt Reference

Draw a regular square pyramid with a square base ABCD and four equilateral triangular faces formed by vertex V. Start by drawing the square base ABCD, then rotate around the central axis from the center O of the base to vertex V to generate the pyramid. Next, find the midpoints N, K, L, and M of each side of the base, and connect these midpoints to vertex V to form the triangular faces and central axis of the pyramid.
The prompt above was compiled from the original drawing commands and is for reference only.