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Prism of 1, 1/2, 1/4, 1/8 Cubes

Prism of 1, 1/2, 1/4, 1/8 Cubes
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2016-02-27 22:16
Solid GeometryGeometric Construction
This example demonstrates the construction of a prism with 1, 1/2, 1/4, 1/8 cubes. Key mathematical concepts include cubes, prisms, and geometric construction. Using GeoGebra commands such as Intersect, Point, Cube, and Prism, various faces and edges of the prism can be constructed. Suitable for middle school and above students to learn solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG_1, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(Circle[G, Distance[C, G], Segment[C, G]]) → I
  6. Cube(C, G, I) → b, J, faceIJNM, faceKLMN, edgeCJ, edgeCG, edgeGI, edgeIJ, edgeCK, edgeJN, edgeKN_1, edgeKL, K, edgeGL, edgeLM, edgeIM, edgeMN, L, M, N, faceCGIJ, faceCJNK, faceCGLK, faceGIML
  7. Point(xAxis) → O
  8. Point(Circle[O, Distance[J, O], Segment[J, O]]) → P
  9. Cube(J, O, P) → c, Q, facePQUT, faceRSTU, edgeJQ, edgeJO, edgeOP, edgePQ_1, edgeJR, edgeQU, edgeRU, edgeRS, R, edgeOS, edgeST_1, edgePT, edgeTU, S, T, U, faceJOPQ, faceJQUR, faceJOSR, faceOPTS
  10. Point(Circle[P, Distance[Q, P], Segment[Q, P]]) → V
  11. Cube(Q, P, V) → d, W, face4, face5, edgeQW_1, edgePQ, edgePV, edgeVW, edgeQZ, edge3, edge5, edge4, Z, edge1, edge6, edge2, edge7, A_1, B_1, C_1, facePQWV, face3, face1, face2
  12. Point(Circle[O, Distance[B, O], Segment[B, O]]) → D_1
  13. Cube(B, O, D_1) → e, E_1, face10, face11, edge8, edgeBO, edge10, edge12, edge9, edge14, edge16, edge15, F_1, edge11, edge17, edge13, edge18, G_1, H_1, I_1, face6, face8, face7, face9
  14. Point(Circle[W, Distance[Q, W], Segment[Q, W]]) → J_1
  15. Cube(Q, W, J_1) → f, K_1, face16, face17, edge19, edgeQW, edge21, edge23, edge20, edge25, edge27, edge26, L_1, edge22, edge28, edge24, edge29, M_1, N_1, O_1, face12, face14, face13, face15
  16. Point(Circle[N, Distance[K_1, N], Segment[K_1, N]]) → P_1
  17. Cube(K_1, N, P_1) → g, Q_1, face22, face23, edge33, edge30, edge31, edge35, edge34, edge37, edge39, edge38, R_1, edge32, edge40, edge36, edge41, S_1, T_1, U_1, face18, face21, face19, face20
  18. Point(yAxis) → V_1
  19. Point(Circle[V_1, Distance[K, V_1], Segment[K, V_1]]) → W_1
  20. Cube(K, V_1, W_1) → h, Z_1, face28, face29, edge43, edge42, edge45, edge47, edge44, edge49, edge51, edge50, A_2, edge46, edge52, edge48, edge53, B_2, C_2, D_2, face24, face26, face25, face27
  21. Point(Circle[K, Distance[V_1, K], Segment[V_1, K]]) → E_2
  22. Cube(V_1, K, E_2) → i, F_2, face34, face35, edge57, edge54, edge55, edge59, edge58, edge61, edge63, edge62, G_2, edge56, edge64, edge60, edge65, H_2, I_2, J_2, face30, face33, face31, face32
  23. Point(Circle[N, Distance[K, N], Segment[K, N]]) → K_2
  24. Cube(K, N, K_2) → j, L_2, face40, face41, edge66, edgeKN, edge68, edge70, edge67, edge72, edge74, edge73, M_2, edge69, edge75, edge71, edge76, N_2, O_2, P_2, face36, face38, face37, face39
  25. Point(Circle[K_1, Distance[N, K_1], Segment[N, K_1]]) → Q_2
  26. Cube(N, K_1, Q_2) → k, R_2, face46, face47, edge78, edge77, edge80, edge82, edge79, edge84, edge86, edge85, S_2, edge81, edge87, edge83, edge88, T_2, U_2, V_2, face42, face44, face43, face45
  27. Point(Circle[J_1, Distance[K_1, J_1], Segment[K_1, J_1]]) → W_2
  28. Cube(K_1, J_1, W_2) → l, Z_2, face52, face53, edge92, edge89, edge90, edge94, edge93, edge96, edge98, edge97, A_3, edge91, edge99, edge95, edge100, B_3, C_3, D_3, face48, face51, face49, face50
  29. Point(Circle[F_1, Distance[E, F_1], Segment[E, F_1]]) → E_3
  30. Cube(E, F_1, E_3) → m, F_3, face58, face59, edge102, edge101, edge104, edge106, edge103, edge108, edge110, edge109, G_3, edge105, edge111, edge107, edge112, H_3, I_3, J_3, face54, face56, face55, face57
  31. Point(Circle[S, Distance[F_1, S], Segment[F_1, S]]) → K_3
  32. Cube(F_1, S, K_3) → n, L_3, face64, face65, edge116, edge113, edge114, edge118, edge117, edge120, edge122, edge121, M_3, edge115, edge123, edge119, edge124, N_3, O_3, P_3, face60, face63, face61, face62
  33. Point(Circle[T, Distance[S, T], Segment[S, T]]) → Q_3
  34. Cube(S, T, Q_3) → o, R_3, face70, face71, edge125, edgeST, edge127, edge129, edge126, edge131, edge133, edge132, S_3, edge128, edge134, edge130, edge135, T_3, U_3, V_3, face66, face68, face67, face69
  35. Intersect(edge52, edgeDH) → W_3
  36. Point(Circle[E_3, Distance[H, E_3], Segment[H, E_3]]) → Z_3
  37. Cube(H, E_3, Z_3) → p, A_4, face76, face77, edge137, edge136, edge139, edge141, edge138, edge143, edge145, edge144, B_4, edge140, edge146, edge142, edge147, C_4, D_4, E_4, face72, face74, face73, face75
  38. Point(Circle[K_3, Distance[E_3, K_3], Segment[E_3, K_3]]) → F_4
  39. Cube(E_3, K_3, F_4) → q, G_4, face82, face83, edge149, edge148, edge151, edge153, edge150, edge155, edge157, edge156, H_4, edge152, edge158, edge154, edge159, I_4, J_4, K_4, face78, face80, face79, face81
  40. Point(Circle[Q_3, Distance[K_3, Q_3], Segment[K_3, Q_3]]) → L_4
  41. Cube(K_3, Q_3, L_4) → r, M_4, face88, face89, edge161, edge160, edge163, edge165, edge162, edge167, edge169, edge168, N_4, edge164, edge170, edge166, edge171, O_4, P_4, Q_4, face84, face86, face85, face87
  42. Intersect(edge63, edge46) → R_4
  43. Point(Circle[Z_3, Distance[B_2, Z_3], Segment[B_2, Z_3]]) → S_4
  44. Cube(B_2, Z_3, S_4) → s, T_4, face94, face95, edge173, edge172, edge175, edge177, edge174, edge179, edge181, edge180, U_4, edge176, edge182, edge178, edge183, V_4, W_4, Z_4, face90, face92, face91, face93
  45. Point(Circle[F_4, Distance[Z_3, F_4], Segment[Z_3, F_4]]) → A_5
  46. Cube(Z_3, F_4, A_5) → t, B_5, face100, face101, edge185, edge184, edge187, edge189, edge186, edge191, edge193, edge192, C_5, edge188, edge194, edge190, edge195, D_5, E_5, F_5, face96, face98, face97, face99
  47. Point(Circle[L_4, Distance[F_4, L_4], Segment[F_4, L_4]]) → G_5
  48. Cube(F_4, L_4, G_5) → u, H_5, face106, face107, edge197, edge196, edge199, edge201, edge198, edge203, edge205, edge204, I_5, edge200, edge206, edge202, edge207, J_5, K_5, L_5, face102, face104, face103, face105
  49. Point(Circle[B_1, Distance[T, B_1], Segment[T, B_1]]) → M_5
  50. Cube(T, B_1, M_5) → v, N_5, face112, face113, edge209, edge208, edge211, edge213, edge210, edge215, edge217, edge216, O_5, edge212, edge218, edge214, edge219, P_5, Q_5, R_5, face108, face110, face109, face111
  51. Point(Circle[M_5, Distance[Q_3, M_5], Segment[Q_3, M_5]]) → S_5
  52. Cube(Q_3, M_5, S_5) → w, T_5, face118, face119, edge221, edge220, edge223, edge225, edge222, edge227, edge229, edge228, U_5, edge224, edge230, edge226, edge231, V_5, W_5, Z_5, face114, face116, face115, face117
  53. Point(Circle[N_1, Distance[L_4, N_1], Segment[L_4, N_1]]) → A_6
  54. Cube(L_4, N_1, A_6) → a_1, B_6, face124, face125, edge235, edge232, edge233, edge237, edge236, edge239, edge241, edge240, C_6, edge234, edge242, edge238, edge243, D_6, E_6, F_6, face120, face123, face121, face122
  55. Point(zAxis) → J_6
  56. Prism(face59, J_6) → b_1, G_6, edge247, edge246, edge245, edge248, edge250, edge251, edge249, H_6, I_6, face127, face129, face128, face126, face130, edge244
  57. Prism(face65, I_6) → c_1, K_6, edge255, edge254, edge253, edge256, edge258, edge259, edge257, L_6, M_6, face132, face134, face133, face131, face135, edge252
  58. Prism(face71, M_6) → d_1, N_6, edge263, edge262, edge261, edge264, edge266, edge267, edge265, O_6, P_6, face137, face139, face138, face136, face140, edge260
  59. Prism(face113, P_6) → e_1, Q_6, edge271, edge270, edge269, edge272, edge274, edge275, edge273, R_6, S_6, face142, face144, face143, face141, face145, edge268
  60. Point(edgeEF) → T_6
  61. Point(zAxis) → U_6
  62. Prism(face77, G_6) → f_1, V_6, edge279, edge278, edge277, edge280, edge282, edge283, edge281, W_6, Z_6, face147, face149, face148, face146, face150, edge276
  63. Prism(face83, H_6) → g_1, A_7, edge287, edge286, edge285, edge288, edge290, edge291, edge289, B_7, C_7, face152, face154, face153, face151, face155, edge284
  64. Prism(face89, L_6) → h_1, D_7, edge295, edge294, edge293, edge296, edge298, edge299, edge297, E_7, F_7, face157, face159, face158, face156, face160, edge292
  65. Intersect(edge299, edge266) → J_7
  66. Prism(face119, O_6) → i_1, G_7, edge303, edge302, edge301, edge304, edge306, edge307, edge305, H_7, I_7, face162, face164, face163, face161, face165, edge300
  67. Point(zAxis) → K_7
  68. Prism(face95, V_6) → j_1, L_7, edge311, edge310, edge309, edge312, edge314, edge315, edge313, M_7, N_7, face167, face169, face168, face166, face170, edge308
  69. Prism(face101, W_6) → k_1, O_7, edge319, edge318, edge317, edge320, edge322, edge323, edge321, P_7, Q_7, face172, face174, face173, face171, face175, edge316
  70. Prism(face107, B_7) → l_1, R_7, edge327, edge326, edge325, edge328, edge330, edge331, edge329, S_7, T_7, face177, face179, face178, face176, face180, edge324
  71. Point(edge5) → U_7
  72. Prism(face125, E_7) → m_1, V_7, edge335, edge334, edge333, edge336, edge338, edge339, edge337, W_7, Z_7, face182, face184, face183, face181, face185, edge332
  73. Point(yAxis) → D_8
  74. Prism(face34, D_8) → n_1, A_8, edge340, edge342, edge343, edge344, edge346, edge347, edge345, B_8, C_8, face186, face187, face189, face188, face190, edge341
  75. Prism(face94, C_8) → o_1, E_8, edge348, edge350, edge351, edge352, edge354, edge355, edge353, F_8, G_8, face191, face192, face194, face193, face195, edge349
  76. Prism(face100, B_8) → p_1, H_8, edge356, edge358, edge359, edge360, edge362, edge363, edge361, I_8, J_8, face196, face197, face199, face198, face200, edge357
  77. Point(xAxis) → K_8
  78. Point(edgeCG_1) → L_8
  79. Prism(face40, A_8) → q_1, M_8, edge364, edge366, edge367, edge368, edge370, edge371, edge369, N_8, O_8, face201, face202, face204, face203, face205, edge365
  80. Point(edgeKN_1) → P_8
  81. Prism(face46, M_8) → r_1, Q_8, edge372, edge374, edge375, edge376, edge378, edge379, edge377, R_8, S_8, face206, face207, face209, face208, face210, edge373
  82. Prism(face106, H_8) → s_1, T_8, edge380, edge382, edge383, edge384, edge386, edge387, edge385, U_8, V_8, face211, face212, face214, face213, face215, edge381
  83. Prism(face124, R_8) → t_1, W_8, edge388, edge390, edge391, edge392, edge394, edge395, edge393, Z_8, A_9, face216, face217, face219, face218, face220, edge389
  84. Point(edge30) → B_9
  85. Prism(face52, Q_8) → u_1, C_9, edge396, edge398, edge399, edge400, edge402, edge403, edge401, D_9, E_9, face221, face222, face224, face223, face225, edge397
  86. Prism(face4, I_9) → v_1, F_9, edge404, edge406, edge407, edge408, edge410, edge411, edge409, G_9, H_9, face226, face227, face229, face228, face230, edge405
  87. Prism(face15, M_9) → w_1, J_9, edge412, edge414, edge415, edge416, edge418, edge419, edge417, K_9, L_9, face231, face232, face234, face233, face235, edge413
  88. Prism(face50, Q_9) → a_2, N_9, edge420, edge422, edge423, edge424, edge426, edge427, edge425, O_9, P_9, face236, face237, face239, face238, face240, edge421
  89. Point(edge38) → R_9
  90. Point(edge368) → S_9
  91. Prism(face111, H_9) → b_2, T_9, edge428, edge430, edge431, edge432, edge434, edge435, edge433, U_9, V_9, face241, face242, face244, face243, face245, edge429
  92. Point(edge83) → W_9
  93. Point(edge202) → Z_9
  94. Prism(face122, P_9) → c_2, A_{10}, edge436, edge438, edge439, edge440, edge442, edge443, edge441, B_{10}, C_{10}, face246, face247, face249, face248, face250, edge437
  95. Prism(face117, L_9) → d_2, D_{10}, edge444, edge446, edge447, edge448, edge450, edge451, edge449, E_{10}, F_{10}, face251, face252, face254, face253, face255, edge445
  96. Point(edge190) → G_{10}
  97. Point(edge166) → H_{10}
  98. Point(edge71) → I_{10}
  99. Prism(face169, G_8) → e_2, J_{10}, edge452, edge455, edge454, edge456, edge458, edge459, edge457, K_{10}, L_{10}, face256, face257, face259, face258, face260, edge453
  100. Prism(face174, F_8) → f_2, M_{10}, edge460, edge463, edge462, edge464, edge466, edge467, edge465, N_{10}, O_{10}, face261, face262, face264, face263, face265, edge461
  101. Prism(face179, I_8) → g_2, P_{10}, edge468, edge471, edge470, edge472, edge474, edge475, edge473, Q_{10}, R_{10}, face266, face267, face269, face268, face270, edge469
  102. Point(edge242) → S_{10}
  103. Prism(face184, U_8) → h_2, T_{10}, edge476, edge479, edge478, edge480, edge482, edge483, edge481, U_{10}, V_{10}, face271, face272, face274, face273, face275, edge477
  104. Prism(face183, C_{10}) → i_2, W_{10}, edge484, edge487, edge486, edge488, edge490, edge491, edge489, Z_{10}, A_{11}, face276, face277, face279, face278, face280, edge485
  105. Prism(face163, B_{10}) → j_2, B_{11}, edge492, edge495, edge494, edge496, edge498, edge499, edge497, C_{11}, D_{11}, face281, face282, face284, face283, face285, edge493
  106. Prism(face143, V_9) → k_2, E_{11}, edge500, edge503, edge502, edge504, edge506, edge507, edge505, F_{11}, G_{11}, face286, face287, face289, face288, face290, edge501
  107. Prism(face238, W_8) → l_2, H_{11}, edge508, edge512, edge513, edge510, edge514, edge515, edge511, I_{11}, J_{11}, face291, face292, face295, face293, face294, edge509
  108. Prism(face248, Z_8) → m_2, K_{11}, edge516, edge520, edge521, edge518, edge522, edge523, edge519, L_{11}, M_{11}, face296, face297, face300, face298, face299, edge517
  109. Prism(face278, U_{10}) → n_2, N_{11}, edge524, edge526, edge529, edge527, edge530, edge531, edge528, O_{11}, P_{11}, face301, face302, face304, face303, face305, edge525