Oblique Regular Pentagonal Pyramid 3D Solid Model

Oblique Regular Pentagonal Pyramid 3D Solid Model
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2017-01-20 02:24
This GeoGebra example demonstrates an oblique regular pentagonal pyramid, a 3D solid whose base is a regular pentagon but whose apex is not directly above the base center. The core mathematical concepts include solid geometry, the definition of a pyramid, the distinction between oblique and right pyramids, regular polygon bases, lateral triangular faces, and spatial relationships when the apex projection is off-center. Construction highlights: using GeoGebra commands Point to define base vertices A, B and apex-related points C, D, E, F; Polygon to create the regular pentagonal base poly1; and Pyramid to generate the solid from the base and apex, automatically producing lateral faces (faceABCDE, faceCDF, faceDEF, etc.) and edges (edgeCD, edgeDE, etc.). This model is suitable for high school or early college students learning solid geometry to visually explore the apex position, lateral face shapes, and base relationships, as well as for exercises in spatial reasoning and volume formulas.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  3. Point(zAxis) → F
  4. Pyramid(C, D, E, A, B, F) → a, faceABCDE, edgeAB, edgeBC, edgeCF, edgeDF, edgeEF, edgeAF, edgeBF, faceCDF, faceDEF, faceAEF, faceABF, faceBCF, edgeCD, edgeDE, edgeAE

AI Drawing Prompt Reference

Create a 3D model of an oblique regular pentagonal pyramid. The base is a regular pentagon lying on a horizontal plane, with five vertices connected in order. The apex is not directly above the center of the base but is offset to one side, positioned on a vertical axis. Connect the apex to each of the five base vertices with straight lines, forming five triangular lateral faces. The result is a solid with a regular pentagonal base and an off-center apex, illustrating the oblique pyramid's spatial geometry.
The prompt above was compiled from the original drawing commands and is for reference only.