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Soma Cube (240 solutions) – 3D GeoGebra Demonstration

Soma Cube (240 solutions) – 3D GeoGebra Demonstration
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2018-02-13 10:56
SequenceCoordinate GeometrySolid GeometryTransformationGeometric Construction
This GeoGebra example constructs the classic Soma Cube puzzle in 3D, displaying one of its 240 known solutions. The Soma Cube consists of seven irregular polycubes (made of 3 or 4 unit cubes) that must be assembled into a 3×3×3 cube, a classic problem in solid geometry and combinatorial mathematics. Core mathematical concepts include spatial rotation, translation, symmetry, and combinatorial enumeration. Construction highlights: the Sequence command generates sequences of unit cubes, Dilate controls scaling, and lists (listAll, list1, list2) store coordinates and orientations of each piece. Objects A1–A28 and B1–B7 represent individual blocks and auxiliary points, enabling interactive rotation and movement to visualize the solution. Suitable for high school to early university students to enhance spatial reasoning and understand 3D transformations, and also useful as a visual aid for algorithm design (e.g., backtracking search) in puzzle-solving.

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 shape consisting of seven irregular polycubes made of 3 or 4 unit cubes, assembled into a 3×3×3 cube. Show one of its solutions, emphasizing spatial rotation, translation, and symmetry. Some polycubes are scaled larger, and the arrangement should clearly display the combination, suitable for teaching solid geometry and combinatorial mathematics.
The prompt above was compiled from the original drawing commands and is for reference only.