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Stellated truncated octahedron construction

Stellated truncated octahedron construction
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2016-05-02 12:52
Solid GeometryGeometric Construction
In collections My 3D Collection
This example demonstrates the stellation process of a truncated octahedron, involving polyhedra, star polyhedra, and solid geometry concepts. It uses GeoGebra commands stel14sz, stel14kw and objects A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z, A1, B1, C1, D1, E1, F1, A2, B2, C2, D2, E2, F2, A3, B3, C3, D3. Suitable for high school solid geometry learning or mathematical modeling reference.

GeoGebra Commands & Parameters

  1. stel14sz(A1, B1, C1, D1, E1, F1) → G1, H1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, I1, AA1, AB1, AC1, AD1, AE1, AF1, AG1, AH1, AI1, AJ1, J1, K1, L1, M1, N1, O1, P1
  2. stel14sz(A2, B2, C2, D2, E2, F2) → G2, H2, Q2, R2, S2, T2, U2, V2, W2, X2, Y2, Z2, I2, AA2, AB2, AC2, AD2, AE2, AF2, AG2, AH2, AI2, AJ2, J2, K2, L2, M2, N2, O2, P2
  3. stel14sz(A3, B3, C3, D3, E3, F3) → G3, H3, Q3, R3, S3, T3, U3, V3, W3, X3, Y3, Z3, I3, AA3, AB3, AC3, AD3, AE3, AF3, AG3, AH3, AI3, AJ3, J3, K3, L3, M3, N3, O3, P3
  4. stel14sz(A4, B4, C4, D4, E4, F4) → G4, H4, Q4, R4, S4, T4, U4, V4, W4, X4, Y4, Z4, I4, AA4, AB4, AC4, AD4, AE4, AF4, AG4, AH4, AI4, AJ4, J4, K4, L4, M4, N4, O4, P4
  5. stel14sz(A5, B5, C5, D5, E5, F5) → G5, H5, Q5, R5, S5, T5, U5, V5, W5, X5, Y5, Z5, I5, AA5, AB5, AC5, AD5, AE5, AF5, AG5, AH5, AI5, AJ5, J5, K5, L5, M5, N5, O5, P5
  6. stel14sz(A6, B6, C6, D6, E6, F6) → G6, H6, Q6, R6, S6, T6, U6, V6, W6, X6, Y6, Z6, I6, AA6, AB6, AC6, AD6, AE6, AF6, AG6, AH6, AI6, AJ6, J6, K6, L6, M6, N6, O6, P6
  7. stel14sz(A7, B7, C7, D7, E7, F7) → G7, H7, Q7, R7, S7, T7, U7, V7, W7, X7, Y7, Z7, I7, AA7, AB7, AC7, AD7, AE7, AF7, AG7, AH7, AI7, AJ7, J7, K7, L7, M7, N7, O7, P7
  8. stel14sz(A8, B8, C8, D8, E8, F8) → G8, H8, Q8, R8, S8, T8, U8, V8, W8, X8, Y8, Z8, I8, AA8, AB8, AC8, AD8, AE8, AF8, AG8, AH8, AI8, AJ8, J8, K8, L8, M8, N8, O8, P8
  9. stel14kw(A9, B9, C9, D9) → E9, F9, O9, P9, Q9, R9, S9, T9, U9, V9, W9, X9, G9, Y9, Z9, AA9, AB9, AC9, AD9, AE9, AF9, AG9, AH9, H9, AI9, AJ9, I9, J9, K9, L9, M9, N9
  10. stel14kw(A10, B10, C10, D10) → E10, F10, O10, P10, Q10, R10, S10, T10, U10, V10, W10, X10, G10, Y10, Z10, AA10, AB10, AC10, AD10, AE10, AF10, AG10, AH10, H10, AI10, AJ10, I10, J10, K10, L10, M10, N10
  11. stel14kw(A11, B11, C11, D11) → E11, F11, O11, P11, Q11, R11, S11, T11, U11, V11, W11, X11, G11, Y11, Z11, AA11, AB11, AC11, AD11, AE11, AF11, AG11, AH11, H11, AI11, AJ11, I11, J11, K11, L11, M11, N11
  12. stel14kw(A12, B12, C12, D12) → E12, F12, O12, P12, Q12, R12, S12, T12, U12, V12, W12, X12, G12, Y12, Z12, AA12, AB12, AC12, AD12, AE12, AF12, AG12, AH12, H12, AI12, AJ12, I12, J12, K12, L12, M12, N12
  13. stel14kw(A13, B13, C13, D13) → E13, F13, O13, P13, Q13, R13, S13, T13, U13, V13, W13, X13, G13, Y13, Z13, AA13, AB13, AC13, AD13, AE13, AF13, AG13, AH13, H13, AI13, AJ13, I13, J13, K13, L13, M13, N13
  14. stel14kw(A14, B14, C14, D14) → E14, F14, O14, P14, Q14, R14, S14, T14, U14, V14, W14, X14, G14, Y14, Z14, AA14, AB14, AC14, AD14, AE14, AF14, AG14, AH14, H14, AI14, AJ14, I14, J14, K14, L14, M14, N14

AI Drawing Prompt Reference

Create a stellated truncated octahedron, demonstrating the stellation process in solid geometry. Begin by constructing multiple hexagons and pentagons to form the base framework of the truncated octahedron, then extend and connect the vertices to create intricate star-like structures. The final image should display a complex polyhedral shape with numerous faces and edges, showcasing the stellation process and geometric beauty of the solid.
The prompt above was compiled from the original drawing commands and is for reference only.