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Soma Cube (240 Solutions)

Soma Cube (240 Solutions)
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2015-11-09 19:45
SequenceSolid GeometryGeometric Construction
This GeoGebra example demonstrates the Soma cube, involving solid geometry. Using a series of commands such as sequence and dilation, all possible solutions of the Soma cube can be constructed. This example is suitable for teaching and learning geometric construction and solid geometry.

GeoGebra Commands & Parameters

  1. Sequence((list1(i), list1(i + 1), list1(i + 2)), i, 1, Length[list1], 3) → list2
  2. Dilate(B1, explode, (1.5, 1.5, 1.5)) → C1
  3. Dilate(B5, explode, (1.5, 1.5, 1.5)) → C5
  4. Dilate(B9, explode, (1.5, 1.5, 1.5)) → C9
  5. Dilate(B13, explode, (1.5, 1.5, 1.5)) → C13
  6. Dilate(B17, explode, (1.5, 1.5, 1.5)) → C17
  7. Dilate(B21, explode, (1.5, 1.5, 1.5)) → C21
  8. Dilate(B25, explode, (1.5, 1.5, 1.5)) → C25
  9. Cube(C1, C1 + (0, 1, 0), u) → D1, E1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, F1, X1, Y1, Z1, AA1, AB1, G1, H1, I1, J1, K1, L1, M1
  10. Cube(C2, C2 + (0, 1, 0), u) → D2, E2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2, F2, X2, Y2, Z2, AA2, AB2, G2, H2, I2, J2, K2, L2, M2
  11. Cube(C3, C3 + (0, 1, 0), u) → D3, E3, N3, O3, P3, Q3, R3, S3, T3, U3, V3, W3, F3, X3, Y3, Z3, AA3, AB3, G3, H3, I3, J3, K3, L3, M3
  12. Cube(C4, C4 + (0, 1, 0), u) → D4, E4, N4, O4, P4, Q4, R4, S4, T4, U4, V4, W4, F4, X4, Y4, Z4, AA4, AB4, G4, H4, I4, J4, K4, L4, M4
  13. Cube(C5, C5 + (0, 1, 0), u) → D5, E5, N5, O5, P5, Q5, R5, S5, T5, U5, V5, W5, F5, X5, Y5, Z5, AA5, AB5, G5, H5, I5, J5, K5, L5, M5
  14. Cube(C6, C6 + (0, 1, 0), u) → D6, E6, N6, O6, P6, Q6, R6, S6, T6, U6, V6, W6, F6, X6, Y6, Z6, AA6, AB6, G6, H6, I6, J6, K6, L6, M6
  15. Cube(C7, C7 + (0, 1, 0), u) → D7, E7, N7, O7, P7, Q7, R7, S7, T7, U7, V7, W7, F7, X7, Y7, Z7, AA7, AB7, G7, H7, I7, J7, K7, L7, M7
  16. Cube(C8, C8 + (0, 1, 0), u) → D8, E8, N8, O8, P8, Q8, R8, S8, T8, U8, V8, W8, F8, X8, Y8, Z8, AA8, AB8, G8, H8, I8, J8, K8, L8, M8
  17. Cube(C9, C9 + (0, 1, 0), u) → D9, E9, N9, O9, P9, Q9, R9, S9, T9, U9, V9, W9, F9, X9, Y9, Z9, AA9, AB9, G9, H9, I9, J9, K9, L9, M9
  18. Cube(C10, C10 + (0, 1, 0), u) → D10, E10, N10, O10, P10, Q10, R10, S10, T10, U10, V10, W10, F10, X10, Y10, Z10, AA10, AB10, G10, H10, I10, J10, K10, L10, M10
  19. Cube(C11, C11 + (0, 1, 0), u) → D11, E11, N11, O11, P11, Q11, R11, S11, T11, U11, V11, W11, F11, X11, Y11, Z11, AA11, AB11, G11, H11, I11, J11, K11, L11, M11
  20. Cube(C13, C13 + (0, 1, 0), u) → D13, E13, N13, O13, P13, Q13, R13, S13, T13, U13, V13, W13, F13, X13, Y13, Z13, AA13, AB13, G13, H13, I13, J13, K13, L13, M13
  21. Cube(C14, C14 + (0, 1, 0), u) → D14, E14, N14, O14, P14, Q14, R14, S14, T14, U14, V14, W14, F14, X14, Y14, Z14, AA14, AB14, G14, H14, I14, J14, K14, L14, M14
  22. Cube(C15, C15 + (0, 1, 0), u) → D15, E15, N15, O15, P15, Q15, R15, S15, T15, U15, V15, W15, F15, X15, Y15, Z15, AA15, AB15, G15, H15, I15, J15, K15, L15, M15
  23. Cube(C16, C16 + (0, 1, 0), u) → D16, E16, N16, O16, P16, Q16, R16, S16, T16, U16, V16, W16, F16, X16, Y16, Z16, AA16, AB16, G16, H16, I16, J16, K16, L16, M16
  24. Cube(C17, C17 + (0, 1, 0), u) → D17, E17, N17, O17, P17, Q17, R17, S17, T17, U17, V17, W17, F17, X17, Y17, Z17, AA17, AB17, G17, H17, I17, J17, K17, L17, M17
  25. Cube(C18, C18 + (0, 1, 0), u) → D18, E18, N18, O18, P18, Q18, R18, S18, T18, U18, V18, W18, F18, X18, Y18, Z18, AA18, AB18, G18, H18, I18, J18, K18, L18, M18
  26. Cube(C19, C19 + (0, 1, 0), u) → D19, E19, N19, O19, P19, Q19, R19, S19, T19, U19, V19, W19, F19, X19, Y19, Z19, AA19, AB19, G19, H19, I19, J19, K19, L19, M19
  27. Cube(C20, C20 + (0, 1, 0), u) → D20, E20, N20, O20, P20, Q20, R20, S20, T20, U20, V20, W20, F20, X20, Y20, Z20, AA20, AB20, G20, H20, I20, J20, K20, L20, M20
  28. Cube(C21, C21 + (0, 1, 0), u) → D21, E21, N21, O21, P21, Q21, R21, S21, T21, U21, V21, W21, F21, X21, Y21, Z21, AA21, AB21, G21, H21, I21, J21, K21, L21, M21
  29. Cube(C22, C22 + (0, 1, 0), u) → D22, E22, N22, O22, P22, Q22, R22, S22, T22, U22, V22, W22, F22, X22, Y22, Z22, AA22, AB22, G22, H22, I22, J22, K22, L22, M22
  30. Cube(C23, C23 + (0, 1, 0), u) → D23, E23, N23, O23, P23, Q23, R23, S23, T23, U23, V23, W23, F23, X23, Y23, Z23, AA23, AB23, G23, H23, I23, J23, K23, L23, M23
  31. Cube(C24, C24 + (0, 1, 0), u) → D24, E24, N24, O24, P24, Q24, R24, S24, T24, U24, V24, W24, F24, X24, Y24, Z24, AA24, AB24, G24, H24, I24, J24, K24, L24, M24
  32. Cube(C25, C25 + (0, 1, 0), u) → D25, E25, N25, O25, P25, Q25, R25, S25, T25, U25, V25, W25, F25, X25, Y25, Z25, AA25, AB25, G25, H25, I25, J25, K25, L25, M25
  33. Cube(C26, C26 + (0, 1, 0), u) → D26, E26, N26, O26, P26, Q26, R26, S26, T26, U26, V26, W26, F26, X26, Y26, Z26, AA26, AB26, G26, H26, I26, J26, K26, L26, M26
  34. Cube(C27, C27 + (0, 1, 0), u) → D27, E27, N27, O27, P27, Q27, R27, S27, T27, U27, V27, W27, F27, X27, Y27, Z27, AA27, AB27, G27, H27, I27, J27, K27, L27, M27
  35. Cube(C28, C28 + (0, 1, 0), u) → D28, E28, N28, O28, P28, Q28, R28, S28, T28, U28, V28, W28, F28, X28, Y28, Z28, AA28, AB28, G28, H28, I28, J28, K28, L28, M28
  36. Cube(C12, C12 + (0, 1, 0), u) → D12, E12_1, N12_1, O12_1, P12_1, Q12_1, R12_1, S12_1, T12_1, U12_1, V12_1, W12_1, F12_1, X12_1, Y12_1, Z12_1, AA12_1, AB12_1, G12_1, H12_1, I12_1, J12_1, K12_1, L12_1, M12_1

AI Drawing Prompt Reference

Draw a 3D Soma cube made of multiple small cubes. First, create a series of small cubes, then use the scale command to enlarge them by 1.5 times. Next, arrange these cubes in a specific order to form the different parts of the Soma cube. Finally, construct all possible solutions of the Soma cube.
The prompt above was compiled from the original drawing commands and is for reference only.