Sliced Cube

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2021-09-12 18:32

This example demonstrates the dynamic slicing of a cube using GeoGebra, showing how cross-sections change with different cutting planes. It involves concepts like solid geometry, polynomial functions, and coordinate geometry. The construction uses commands such as Intersect, Cube, Sphere, and OrthogonalPlane to create 3D models and animated slices. Suitable for high school students studying 3D geometry and function transformations, or for educational purposes in mathematical modeling.

GeoGebra Commands & Parameters

Intersect(yAxis, xAxis) → A
Point(Circle[B, Distance[C, B], Segment[C, B]]) → D
Cube(C, B, D) → b, E, faceDEIH, faceFGHI, edgeCE, edgeBC, edgeBD, edgeDE, edgeCF, edgeEI, edgeFI, edgeFG, F, edgeBG, edgeGH, edgeDH, edgeHI, G, H, I, faceBCED, faceCEIF, faceBCFG, faceBDHG
Sphere(A, a) → c
Line(G, H) → f
Line(F, I) → g
Line(H, I) → h
Line(G, F) → i
Line(G, B) → j
Line(H, D) → k
Line(B, D) → l
Line(D, E) → m
Line(C, B) → n
Line(E, C) → p
Intersect(p, xOyPlane) → J
Intersect(p, xOyPlane) → K
Line(I, E) → f_2
Line(F, C) → g_2
Intersect(zAxis, c) → L, M
Intersect(yAxis, c) → N, O
Intersect(xAxis, c, 2) → P
Line(C, B) → s
Line(F, G) → t
Line(I, H) → d
Line(E, D) → e
Line(G, H) → f_1
Line(F, I) → g_1
Line(E, C) → h_1
Line(D, B) → i_1
Line(F, C) → q
Line(G, B) → r
Line(H, D) → j_1
Line(I, E) → k_1
OrthogonalPlane(M, k_1) → p_1
Intersect(r, p_1) → Q
Intersect(j_1, p_1) → R
Intersect(k_1, p_1) → S
Intersect(q, p_1) → T
Sphere(M, 2) → o
Intersect(zAxis, o, 2) → U
OrthogonalPlane(U, k_1) → q_1
Intersect(r, q_1) → V
Intersect(q, q_1) → W
Intersect(k_1, q_1) → Z
Intersect(j_1, q_1) → A_1
Mirror(V, g_3) → V'
Mirror(W, g_3) → W'
Mirror(Q, g_3) → Q'
Mirror(T, g_3) → T'
Mirror(R, g_3) → R'
Mirror(S, g_3) → S'
Mirror(Z, g_3) → Z'
Line(O, N) → l_1
Rotate(A_1, -90°, l_1) → B_1
Rotate(V, -90°, l_1) → V'_{1}
Rotate(Z, -90°, l_1) → Z'_{1}
Rotate(W, -90°, l_1) → W'_{1}
Rotate(Q, -90°, l_1) → Q'_{1}
Rotate(R, -90°, l_1) → R'_{1}
Rotate(S, -90°, l_1) → S'_{1}
Rotate(T, -90°, l_1) → T'_{1}
Mirror(B_1, eq1) → C_1
Mirror(Z'_{1}, eq1) → D_1
Mirror(W'_{1}, eq1) → E_1
Mirror(V'_{1}, eq1) → F_1
Mirror(Q'_{1}, eq1) → G_1
Mirror(T'_{1}, eq1) → H_1
Mirror(S'_{1}, eq1) → I_1
Mirror(R'_{1}, eq1) → J_1
Rotate(Z, -90°, s_1) → Z'_{2}
Rotate(W, -90°, s_1) → W'_{2}
Rotate(V, -90°, s_1) → V'_{2}
Rotate(A_1, -90°, s_1) → K_1
Rotate(Q, -90°, s_1) → Q'_{2}
Rotate(R, -90°, s_1) → R'_{2}
Rotate(S, -90°, s_1) → S'_{2}
Rotate(T, -90°, s_1) → T'_{2}
Mirror(Q'_{2}, f_3) → L_1
Mirror(V'_{2}, f_3) → M_1
Mirror(R'_{2}, f_3) → N_1
Mirror(K_1, f_3) → O_1
Mirror(T'_{2}, f_3) → P_1
Mirror(S'_{2}, f_3) → Q_1
Mirror(Z'_{2}, f_3) → R_1
Mirror(W'_{2}, f_3) → S_1
Line(Z, W) → m_1
Line(S, T) → n_1
Line(R, Q) → t_1
Line(A_1, V) → a_1
Line(Q'_{1}, R'_{1}) → b_1
Line(V'_{1}, B_1) → c_1
Line(W'_{1}, Z'_{1}) → d_1
Line(T'_{1}, S'_{1}) → e_1
Intersect(e_1, t_1) → T_1
Intersect(a_1, b_1) → U_1
Intersect(c_1, a_1) → V_1
Intersect(c_1, t_1) → W_1
Intersect(n_1, d_1) → Z_1
Intersect(n_1, e_1) → A_2
Intersect(t_1, b_1) → B_2
Intersect(e_1, m_1) → C_2
Intersect(d_1, m_1) → D_2
Rotate(W_1, 90°, l_1) → E_2
Rotate(Z_1, 90°, l_1) → F_2
Rotate(A_2, 90°, l_1) → G_2
Rotate(B_2, 90°, l_1) → H_2
Rotate(V_1, 90°, l_1) → I_2
Rotate(D_2, 90°, l_1) → J_2
Rotate(C_2, 90°, l_1) → K_2
Rotate(U_1, 90°, l_1) → L_2
Polygon(J_2, K_2, G_2, F_2) → q1, j_2, k_2, h_2, i_2
Polygon(I_2, L_2, H_2, E_2) → q2, l_2, m_2, n_2, e_2
Polygon(U_1, B_2, W_1, V_1) → q3, u_1, b_2, w_1, v_1
Polygon(C_2, A_2, Z_1, D_2) → q4, c_2, a_2, z_1, d_2
Mirror(I_2, g_3) → M_2
Mirror(E_2, g_3) → N_2
Mirror(L_2, g_3) → O_2
Mirror(H_2, g_3) → P_2
Mirror(q2, g_3) → q2'
Mirror(q1, g_3) → q1'
Mirror(J_2, g_3) → Q_2
Mirror(F_2, g_3) → R_2
Mirror(G_2, g_3) → S_2
Mirror(K_2, g_3) → T_2
Mirror(q3, g_3) → q3'
Mirror(q4, g_3) → q4'
Mirror(U_1, g_3) → U_2
Mirror(V_1, g_3) → V_2
Mirror(B_2, g_3) → W_2
Mirror(D_2, g_3) → Z_2
Mirror(C_2, g_3) → A_3
Mirror(A_2, g_3) → B_3
Mirror(Z_1, g_3) → C_3
Midpoint(A_1, W) → D_3
Line(D_3, L) → p_2
Rotate(q2, 90°, p_2) → q2'_{1}
Rotate(q1, 90°, p_2) → q1'_{1}
Rotate(I_2, 90°, p_2) → E_3
Rotate(E_2, 90°, p_2) → F_3
Rotate(L_2, 90°, p_2) → G_3
Rotate(H_2, 90°, p_2) → H_3
Rotate(J_2, 90°, p_2) → I_3
Rotate(F_2, 90°, p_2) → J_3
Rotate(K_2, 90°, p_2) → K_3
Rotate(G_2, 90°, p_2) → L_3
Mirror(q2'_{1}, g_3) → q5
Mirror(q1'_{1}, g_3) → q6
Mirror(K_3, g_3) → M_3
Mirror(L_3, g_3) → N_3
Mirror(J_3, g_3) → O_3
Mirror(I_3, g_3) → P_3
Mirror(H_3, g_3) → Q_3
Mirror(E_3, g_3) → R_3
Mirror(G_3, g_3) → S_3
Mirror(q2'_{1}, f_3) → q7
Mirror(q1'_{1}, f_3) → q8
Mirror(q6, f_3) → q6'
Mirror(R_3, f_3) → T_3
Mirror(q5, f_3) → q5'
Mirror(I_3, f_3) → U_3
Mirror(K_3, f_3) → V_3
Mirror(L_3, f_3) → W_3
Mirror(J_3, f_3) → Z_3
Mirror(E_3, f_3) → A_4
Mirror(F_3, f_3) → B_4
Mirror(H_3, f_3) → C_4
Mirror(G_3, f_3) → D_4
Mirror(S_3, f_3) → E_4
Mirror(M_3, f_3) → F_4
Mirror(P_3, f_3) → G_4
Mirror(Q_3, f_3) → H_4
Mirror(O_3, f_3) → I_4
Mirror(N_3, f_3) → J_4
Mirror(F_3, g_3) → K_4
Line(A_4, U_3) → q_2
Line(B_4, Z_3) → r_2
Line(C_4, W_3) → s_2
Line(D_4, V_3) → t_2
Line(E_2, F_2) → h_3
Line(I_2, J_2) → i_3
Line(L_2, K_2) → j_3
Line(H_2, G_2) → k_3
Intersect(h_3, q_2) → L_4
Intersect(q_2, i_3) → M_4
Intersect(r_2, i_3) → N_4
Intersect(s_2, j_3) → O_4
Intersect(k_3, s_2) → P_4
Intersect(k_3, t_2) → Q_4
Intersect(r_2, h_3) → R_4
Intersect(t_2, j_3) → S_4
Polygon(M_4, S_4, O_4, N_4) → q9, m_4, s_4, o_4, n_4
Polygon(L_4, Q_4, P_4, R_4) → q10, l_4, q_4, p_4, r_4
Mirror(q9, f_3) → q9'
Mirror(q10, f_3) → q10'
Mirror(M_4, f_3) → T_4
Mirror(N_4, f_3) → U_4
Mirror(S_4, f_3) → V_4
Mirror(O_4, f_3) → W_4
Mirror(L_4, f_3) → Z_4
Mirror(R_4, f_3) → A_5
Mirror(P_4, f_3) → B_5
Mirror(Q_4, f_3) → C_5
Mirror(q9', eq1) → q9''
Mirror(U_4, eq1) → D_5
Mirror(W_4, eq1) → E_5
Mirror(V_4, eq1) → F_5
Mirror(T_4, eq1) → G_5
Mirror(q10', eq1) → q10''
Mirror(Z_4, eq1) → H_5
Mirror(C_5, eq1) → I_5
Mirror(A_5, eq1) → J_5
Mirror(B_5, eq1) → K_5
Mirror(q9'', f_3) → q9'''
Mirror(q10'', f_3) → q10'''
Mirror(D_5, f_3) → L_5
Mirror(G_5, f_3) → M_5
Mirror(F_5, f_3) → N_5
Mirror(H_5, f_3) → O_5
Mirror(E_5, f_3) → P_5
Mirror(I_5, f_3) → Q_5
Mirror(K_5, f_3) → R_5
Mirror(J_5, f_3) → S_5
Mirror(q9, g_3) → q9'_{1}
Mirror(q10, g_3) → q10'_{1}
Mirror(O_4, g_3) → T_5
Mirror(S_4, g_3) → U_5
Mirror(M_4, g_3) → V_5
Mirror(N_4, g_3) → W_5
Mirror(R_4, g_3) → Z_5
Mirror(L_4, g_3) → A_6
Mirror(Q_4, g_3) → B_6
Mirror(P_4, g_3) → C_6
Mirror(q10''', g_3) → q11
Mirror(q9''', g_3) → q12
Mirror(L_5, g_3) → D_6
Mirror(M_5, g_3) → E_6
Mirror(N_5, g_3) → F_6
Mirror(P_5, g_3) → G_6
Mirror(Q_5, g_3) → H_6
Mirror(O_5, g_3) → I_6
Mirror(S_5, g_3) → J_6
Mirror(R_5, g_3) → K_6
Mirror(q9', g_3) → q9''_{1}
Mirror(q10', g_3) → q10''_{1}
Mirror(U_4, g_3) → L_6
Mirror(T_4, g_3) → M_6
Mirror(V_4, g_3) → N_6
Mirror(W_4, g_3) → O_6
Mirror(Z_4, g_3) → P_6
Mirror(A_5, g_3) → Q_6
Mirror(B_5, g_3) → R_6
Mirror(C_5, g_3) → S_6
Mirror(q9'', g_3) → q9'''_{1}
Mirror(q10'', g_3) → q10'''_{1}
Mirror(E_5, g_3) → T_6
Mirror(F_5, g_3) → U_6
Mirror(G_5, g_3) → V_6
Mirror(D_5, g_3) → W_6
Mirror(I_5, g_3) → Z_6
Mirror(H_5, g_3) → A_7
Mirror(J_5, g_3) → B_7
Mirror(K_5, g_3) → C_7
Polygon(R'_{2}, S'_{2}, Z'_{2}, K_1) → q13, r'_{2}, s'_{2}, z'_{2}, l_3
Polygon(Q'_{2}, T'_{2}, W'_{2}, V'_{2}) → q14, q'_{2}, t'_{2}, w'_{2}, v'_{2}
Polygon(A_1, R, S, Z) → q15, m_3, r_3, s_3, z_2
Polygon(V, Q, T, W) → q16, v, q_3, t_3, w
Polygon(K_2, L_2, I_2, J_2) → q17, n_3, p_3, a_3, b_3
Polygon(L_2, H_2, G_2, K_2) → q18, c_3, d_3, e_3, f_4
Polygon(J_2, I_2, E_2, F_2) → q19, g_4, h_4, i_4, j_4
Polygon(F_2, G_2, H_2, E_2) → q20, k_4, t_4, a_4, b_4
Polygon(J_1, C_1, F_1, G_1) → q21, c_4, d_4, e_4, f_5
Polygon(I_1, H_1, E_1, D_1) → q22, g_5, h_5, i_5, j_5
Polygon(Z'_{1}, W'_{1}, T'_{1}, S'_{1}) → q23, z'_{1}, w'_{1}, t'_{1}, s'_{1}
Polygon(B_1, V'_{1}, Q'_{1}, R'_{1}) → q24, k_5, v'_{1}, q'_{1}, r'_{1}
Polygon(L_1, P_1, S_1, M_1) → q25, l_5, m_5, n_5, p_5
Polygon(N_1, Q_1, R_1, O_1) → q26, q_5, r_5, s_5, o_1
Polygon(G_1, H_1, E_1, F_1) → q27, t_5, a_5, b_5, c_5
Polygon(J_1, I_1, H_1, G_1) → q28, d_5, e_5, f_6, g_6
Polygon(C_1, D_1, I_1, J_1) → q29, h_6, i_6, j_6, k_6
Polygon(C_1, F_1, E_1, D_1) → q30, l_6, m_6, n_6, p_6
Polygon(I_3, E_3, F_3, J_3) → q31, q_6, r_6, s_6, t_6
Polygon(K_3, G_3, E_3, I_3) → q32, a_6, b_6, c_6, d_6
Polygon(K_3, L_3, H_3, G_3) → q33, e_6, f_7, g_7, h_7
Polygon(J_3, L_3, H_3, F_3) → q34, i_7, j_7, k_7, l_7
Polygon(V_4, C_5, Z_4, T_4) → q35, v_4, m_7, z_4, n_7
Polygon(U_4, A_5, Z_4, T_4) → q36, u_4, p_7, q_7, r_7
Polygon(V_4, C_5, B_5, W_4) → q37, s_7, t_7, a_7, w_4
Polygon(H_5, G_5, D_5, J_5) → q38, b_7, c_7, d_7, e_7
Polygon(K_5, E_5, F_5, I_5) → q39, f_8, g_8, h_8, i_8
Polygon(H_5, I_5, F_5, G_5) → q40, j_8, k_8, l_8, m_8
Polygon(J_5, K_5, E_5, D_5) → q41, n_8, p_8, q_8, r_8
Polygon(B_2, A_2, C_2, U_1) → q42, s_8, t_8, a_8, b_8
Polygon(V_1, W_1, Z_1, D_2) → q43, c_8, d_8, e_8, f_9
Polygon(W_1, B_2, A_2, Z_1) → q44, g_9, h_9, i_9, j_9
Polygon(U_1, C_2, D_2, V_1) → q45, k_9, l_9, m_9, n_9
Polygon(A_1, V, W, Z) → q46, p_9, v_2, w_2, z_3
Polygon(R, Q, T, S) → q47, r_9, q_9, t_9, s_9
Polygon(Z, S, T, W) → q48, z_5, s_{10}, t_{10}, w_3
Polygon(A_1, R, Q, V) → q49, a_9, r_{10}, q_{10}, v_3
Polygon(S_5, L_5, M_5, O_5) → q50, b_9, c_9, d_9, o_5
Polygon(R_5, P_5, N_5, Q_5) → q51, e_9, f_{10}, g_{10}, h_{10}
Polygon(R_5, P_5, L_5, S_5) → q52, i_{10}, j_{10}, k_{10}, l_{10}
Polygon(O_5, Q_5, N_5, M_5) → q53, m_{10}, n_{10}, p_{10}, a_{10}
Polygon(D_4, V_3, W_3, C_4) → q54, b_{10}, c_{10}, d_{10}, e_{10}
Polygon(U_3, V_3, D_4, A_4) → q55, u_3, f_{11}, g_{11}, h_{11}
Polygon(Z_3, B_4, C_4, W_3) → q56, i_{11}, j_{11}, k_{11}, l_{11}
Polygon(Z_3, B_4, A_4, U_3) → q57, m_{11}, n_{11}, p_{11}, q_{11}
Polygon(Q_4, S_4, M_4, L_4) → q58, r_{11}, s_{11}, t_{11}, a_{11}
Polygon(S_4, O_4, P_4, Q_4) → q59, b_{11}, c_{11}, d_{11}, e_{11}
Polygon(N_4, R_4, P_4, O_4) → q60, f_{12}, g_{12}, h_{12}, i_{12}
Polygon(N_4, R_4, L_4, M_4) → q61, j_{12}, k_{12}, l_{12}, m_{12}
Polygon(M_2, Q_2, R_2, N_2) → q62, n_{12}, p_{12}, q_{12}, r_{12}
Polygon(O_2, M_2, Q_2, T_2) → q63, o_2, s_{12}, t_{12}, a_{12}
Polygon(P_2, N_2, R_2, S_2) → q64, b_{12}, c_{12}, d_{12}, e_{12}
Polygon(P_2, O_2, T_2, S_2) → q65, f_{13}, g_{13}, h_{13}, i_{13}
Polygon(C_6, T_5, U_5, B_6) → q66, j_{13}, k_{13}, u_5, l_{13}
Polygon(C_6, Z_5, W_5, T_5) → q67, m_{13}, n_{13}, w_5, p_{13}
Polygon(B_6, A_6, V_5, U_5) → q68, q_{13}, r_{13}, v_5, s_{13}
Polygon(O_6, R_6, Q_6, L_6) → q69, o_6, t_{13}, a_{13}, b_{13}
Polygon(P_6, Q_6, L_6, M_6) → q70, c_{13}, d_{13}, e_{13}, f_{14}
Polygon(N_6, M_6, P_6, S_6) → q71, g_{14}, h_{14}, i_{14}, j_{14}
Polygon(N_6, O_6, R_6, S_6) → q72, k_{14}, l_{14}, m_{14}, n_{14}
Polygon(K_4, O_3, P_3, R_3) → q73, p_{14}, o_3, q_{14}, r_{14}
Polygon(N_3, O_3, K_4, Q_3) → q74, s_{14}, t_{14}, a_{14}, b_{14}
Polygon(M_3, S_3, R_3, P_3) → q75, c_{14}, d_{14}, e_{14}, f_{15}
Polygon(N_3, M_3, S_3, Q_3) → q76, g_{15}, h_{15}, i_{15}, j_{15}
Polygon(E_6, I_6, J_6, D_6) → q77, k_{15}, l_{15}, m_{15}, n_{15}
Polygon(G_6, D_6, J_6, K_6) → q78, p_{15}, q_{15}, r_{15}, s_{15}
Polygon(F_6, H_6, K_6, G_6) → q79, t_{15}, a_{15}, b_{15}, c_{15}
Polygon(W_6, B_7, C_7, T_6) → q80, w_6, d_{15}, e_{15}, f_{16}
Polygon(V_6, W_6, B_7, A_7) → q81, v_6, g_{16}, h_{16}, i_{16}
Polygon(U_6, Z_6, C_7, T_6) → q82, u_6, z_6, j_{16}, k_{16}
Polygon(U_6, V_6, A_7, Z_6) → q83, l_{16}, m_{16}, n_{16}, p_{16}
Polygon(S', Z', W', T') → q84, s', z', w', t'
Polygon(P_1, Q_1, N_1, L_1) → q85, q_{16}, r_{16}, s_{16}, t_{16}
Polygon(M_1, O_1, R_1, S_1) → q86, a_{16}, b_{16}, c_{16}, d_{16}
Polygon(P_1, Q_1, R_1, S_1) → q87, e_{16}, f_{17}, g_{17}, h_{17}
Polygon(L_1, M_1, O_1, N_1) → q88, i_{17}, j_{17}, k_{17}, l_{17}
Mirror(A_1, g_3) → D_7
Polygon(D_7, Z', W', V') → q89, m_{17}, n_{17}, p_{17}, v'
Polygon(Q', V', W', T') → q90, q', q_{17}, r_{17}, s_{17}
Polygon(R', D_7, V', Q') → q91, r', t_{17}, a_{17}, b_{17}
Polygon(R', S', Z', D_7) → q92, c_{17}, d_{17}, e_{17}, f_{18}
Mirror(B_4, g_3) → E_7
Polygon(I_4, E_7, H_4, J_4) → q93, g_{18}, h_{18}, i_{18}, j_{18}
Polygon(J_4, F_4, E_4, H_4) → q94, k_{18}, l_{18}, m_{18}, n_{18}
Polygon(I_4, G_4, T_3, E_7) → q95, p_{18}, q_{18}, r_{18}, s_{18}
Polygon(F_4, G_4, T_3, E_4) → q96, t_{18}, a_{18}, b_{18}, c_{18}
Mirror(W_1, g_3) → F_7
Polygon(B_3, W_2, F_7, C_3) → q97, d_{18}, e_{18}, f_{19}, g_{19}
Polygon(A_3, U_2, W_2, B_3) → q98, h_{19}, u_2, i_{19}, j_{19}
Polygon(A_3, U_2, V_2, Z_2) → q99, k_{19}, l_{19}, m_{19}, n_{19}
Polygon(C_3, Z_2, V_2, F_7) → q100, p_{19}, q_{19}, r_{19}, s_{19}
Polygon(S'_{2}, T'_{2}, W'_{2}, Z'_{2}) → q101, t_{19}, a_{19}, b_{19}, c_{19}
Polygon(R'_{2}, Q'_{2}, T'_{2}, S'_{2}) → q102, d_{19}, e_{19}, f_{20}, g_{20}
Polygon(R'_{2}, K_1, V'_{2}, Q'_{2}) → q103, h_{20}, i_{20}, j_{20}, k_{20}
Polygon(K_1, Z'_{2}, W'_{2}, V'_{2}) → q104, l_{20}, m_{20}, n_{20}, p_{20}
Polygon(T'_{1}, Q'_{1}, R'_{1}, S'_{1}) → q105, q_{20}, r_{20}, s_{20}, t_{20}
Polygon(Z'_{1}, B_1, R'_{1}, S'_{1}) → q106, a_{20}, b_{20}, c_{20}, d_{20}
Polygon(T'_{1}, Q'_{1}, V'_{1}, W'_{1}) → q107, e_{20}, f_{21}, g_{21}, h_{21}
Polygon(Z'_{1}, B_1, V'_{1}, W'_{1}) → q108, i_{21}, j_{21}, k_{21}, l_{21}
Line(M_5, N_5) → m_{21}
Line(L_5, P_5) → n_{21}
Line(S_5, R_5) → p_{21}
Line(O_5, Q_5) → q_{21}
Line(K_1, V'_{2}) → r_{21}
Line(Z'_{2}, W'_{2}) → s_{21}
Line(S'_{2}, T'_{2}) → t_{21}
Line(R'_{2}, Q'_{2}) → a_{21}
Intersect(q_{21}, s_{21}) → G_7
Intersect(s_{21}, m_{21}) → H_7
Intersect(n_{21}, t_{21}) → I_7
Intersect(p_{21}, t_{21}) → J_7
Intersect(q_{21}, r_{21}) → K_7
Intersect(p_{21}, a_{21}) → L_7
Intersect(a_{21}, n_{21}) → M_7
Intersect(r_{21}, m_{21}) → N_7
Polygon(G_7, H_7, I_7, J_7) → q109, b_{21}, c_{21}, d_{21}, e_{21}
Polygon(K_7, N_7, M_7, L_7) → q110, f_{22}, g_{22}, h_{22}, i_{22}
Midpoint(J_1, H_1) → O_7
Mirror(q110, eq1) → q110'
Mirror(q109, eq1) → q109'
Mirror(K_7, eq1) → P_7
Mirror(L_7, eq1) → Q_7
Mirror(M_7, eq1) → R_7
Mirror(N_7, eq1) → S_7
Mirror(G_7, eq1) → T_7
Mirror(J_7, eq1) → U_7
Mirror(I_7, eq1) → V_7
Mirror(H_7, eq1) → W_7
Polygon(L_7, J_7, I_7, M_7) → q111, j_{22}, k_{22}, l_{22}, m_{22}
Polygon(K_7, G_7, H_7, N_7) → q112, n_{22}, p_{22}, q_{22}, r_{22}
Polygon(K_7, G_7, J_7, L_7) → q113, s_{22}, t_{22}, a_{22}, b_{22}
Polygon(M_7, N_7, H_7, I_7) → q114, c_{22}, d_{22}, e_{22}, f_{23}
Polygon(S_7, W_7, V_7, R_7) → q115, g_{23}, w_7, v_7, h_{23}
Polygon(R_7, V_7, U_7, Q_7) → q116, i_{23}, j_{23}, u_7, k_{23}
Polygon(P_7, T_7, U_7, Q_7) → q117, l_{23}, m_{23}, n_{23}, p_{23}
Polygon(S_7, W_7, T_7, P_7) → q118, q_{23}, r_{23}, s_{23}, t_{23}
Mirror(q112, f_3) → q112'
Mirror(q111, f_3) → q111'
Mirror(N_7, f_3) → Z_7
Mirror(K_7, f_3) → A_8
Mirror(H_7, f_3) → B_8
Mirror(G_7, f_3) → C_8
Mirror(M_7, f_3) → D_8
Mirror(I_7, f_3) → E_8
Mirror(J_7, f_3) → F_8
Mirror(L_7, f_3) → G_8
Polygon(D_8, Z_7, A_8, G_8) → q119, a_{23}, z_7, b_{23}, c_{23}
Polygon(F_8, C_8, A_8, G_8) → q120, d_{23}, e_{23}, f_{24}, g_{24}
Polygon(F_8, C_8, B_8, E_8) → q121, h_{24}, i_{24}, j_{24}, k_{24}
Polygon(D_8, E_8, B_8, Z_7) → q122, l_{24}, m_{24}, n_{24}, p_{24}
Mirror(q115, f_3) → q115'
Mirror(q117, f_3) → q117'
Mirror(P_7, f_3) → H_8
Mirror(S_7, f_3) → I_8
Mirror(R_7, f_3) → J_8
Mirror(Q_7, f_3) → K_8
Mirror(W_7, f_3) → L_8
Mirror(T_7, f_3) → M_8
Mirror(U_7, f_3) → N_8
Mirror(V_7, f_3) → O_8
Polygon(N_8, O_8, J_8, K_8) → q123, q_{24}, o_8, r_{24}, s_{24}
Polygon(N_8, O_8, L_8, M_8) → q124, t_{24}, a_{24}, b_{24}, c_{24}
Polygon(K_8, H_8, I_8, J_8) → q125, d_{24}, e_{24}, f_{25}, g_{25}
Polygon(H_8, M_8, L_8, I_8) → q126, h_{25}, i_{25}, j_{25}, k_{25}

AI Drawing Prompt Reference

Create a 3D model of a cube being sliced by a sphere and multiple planes. Start with a sphere centered near the origin with adjustable radius, then construct a cube intersecting the sphere. Define several orthogonal planes that cut through different edges of the cube, forming varying polygonal cross-sections. Show the intersection points between the sphere and coordinate axes, along with the sequence of intersection points between planes and cube edges. Use sliders to control the sphere radius or plane positions, observing how the cross-sectional shapes inside the cube change dynamically with cutting positions, demonstrating the relationship between solid geometry sections and function transformations.

The prompt above was compiled from the original drawing commands and is for reference only.