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Inscribed Tetrahedral Triangular Prisms

Inscribed Tetrahedral Triangular Prisms
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2018-06-01 04:50
Solid GeometryTransformationGeometric Construction
This example demonstrates the inscribed structure of tetrahedral triangular prisms. Key mathematical concepts include solid geometry, specifically triangular prisms and tetrahedra. The construction uses GeoGebra commands such as Point, Rotate, Octahedron, Prism, etc. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Rotate(A, (2 * π / 3)) → A'
  3. Point(Circle[Midpoint[A, A'], (Distance[A, A'] * sqrt(3) / 2), Segment[A, A']]) → B
  4. Octahedron(A, A', B) → a, C, faceBDE, faceCDE, edgeAB, edgeAA', edgeA'B, edgeAE, edgeBE, edgeAC, edgeCE, edgeA'C, D, edgeA'D, edgeCD, edgeBD, edgeDE, E, faceAA'B, faceABE, faceACE, faceAA'C, faceA'CD, faceA'BD
  5. Prism(faceA'BD, g) → b, F, edgeDH, edgeFG, edgeGH, edgeFH, G, H, faceA'BFG, faceA'DHG, faceBDHF, faceFGH, edgeBF, edgeA'G
  6. Prism(faceA'CD, g) → c, I, edgeCK, edgeIJ, edgeJK, edgeIK, J, K, faceA'DIJ, faceA'CKJ, faceCDIK, faceIJK, edgeDI, edgeA'J
  7. Prism(faceAA'B, g) → d, L, edgeA'N, edgeLM, edgeMN, edgeLN, M, N, faceABLM, faceAA'NM, faceA'BLN, faceLMN, edgeBL, edgeAM
  8. Prism(faceAA'C, g) → e, O, edgeCQ, edgeOP, edgePQ, edgeOQ, P, Q, faceAA'OP, faceACQP, faceA'CQO, faceOPQ, edgeA'O, edgeAP
  9. Prism(faceABE, g) → f, R, edgeBT, edgeRS, edgeST, edgeRT, S, T, faceAERS, faceABTS, faceBERT, faceRST, edgeER, edgeAS
  10. Prism(faceACE, g) → h, U, edgeEW, edgeUV, edgeVW, edgeUW, V, W, faceACUV, faceAEWV, faceCEWU, faceUVW, edgeCU, edgeAV
  11. Prism(faceACE, g) → i, Z, edge2, edge3, edge5, edge4, A_1, B_1, face2, face3, face4, face1, edgeCZ, edge1
  12. Prism(faceBDE, g) → j, C_1, edge7, edge9, edge11, edge10, D_1, E_1, face7, face6, face8, face5, edge8, edge6
  13. Prism(faceCDE, g) → k, F_1, edge12, edge15, edge17, edge16, G_1, H_1, face12, face10, face11, face9, edge14, edge13