Points, Planes, Pyramids, and Lines

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2012-11-14 21:00

In collections Points, Lines & Planes

This example demonstrates the generation and transformation of various geometric figures including planes, pyramids, and lines by manipulating points. It involves core mathematical concepts such as point-line-plane relationships, spatial geometry, and vector operations. Key GeoGebra commands and objects used in the construction include Circle, Line, OrthogonalLine, Intersect, Polygon, Distance, Rotate, Dilate, Midpoint, If, Segment, Vector, and Textfield. Suitable for high school and above, this tool is ideal for teaching and exploring solid geometry, vectors, and analytical geometry.

GeoGebra Commands & Parameters

Circle(CC, br) → e
Circle(CC, l) → d
Line(AA, BB) → a
OrthogonalLine(CC, a) → b
Intersect(e, b) → F, G
OrthogonalLine(F, b) → h
OrthogonalLine(G, b) → f_{12}
OrthogonalLine(CC, b) → c
Intersect(d, c) → D, E
OrthogonalLine(E, c) → i
Intersect(h, i) → K
Intersect(f_{12}, i) → H
OrthogonalLine(D, c) → g
Intersect(g, h) → J
Intersect(g, f_{12}) → I
Polygon(H, I, J, K) → mangekant1, h_1, i_1, j, k
OrthogonalLine(Rotate, h_1) → m
Intersect(h_1, m) → M
Distance(Rotate, M) → avstandLM
OrthogonalLine(Rotate, k) → n
Intersect(k, n) → N
Distance(Rotate, N) → avstandLN
Circle(O, size) → r
OrthogonalLine(O, a) → p
Intersect(r, p) → R, S
OrthogonalLine(R, p) → a_1
OrthogonalLine(O, p) → q
Intersect(r, q) → P, Q
OrthogonalLine(P, q) → t
Intersect(a_1, t) → V
Rotate(V, ho, O) → V'
OrthogonalLine(V', q) → j_1
Intersect(q, j_1) → C_1
Dilate(V', l1, C_1) → V''
OrthogonalLine(Q, q) → b_1
Intersect(a_1, b_1) → W
Rotate(W, ho, O) → W'
OrthogonalLine(W', q) → l_1
Intersect(l_1, q) → A_1
Dilate(W', l1, A_1) → W''
Midpoint(W'', V'') → D_1
Distance(O, D_1) → avstandOD1
If(((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)) ∧ ((-π) / 2 < ho) ∧ (ho < π / 2) ∨ ((-π) / 2 < ve) ∧ (ve < π / 2) ∧ ((-π < ho) ∧ (ho < (-π) / 2) ∨ (π / 2 < ho) ∧ (ho < π)), van / (size - xp) + 3, (-van) / (size - xp) - 3) → ix
If((-π < ve) ∧ (ve < (-π) / 2) ∨ (0 < ve) ∧ (ve < π / 2), (-van) / (size - zp) - 3, van / (size - zp) + 3) → iz
OrthogonalLine(S, p) → s
Intersect(s, b_1) → T
Intersect(s, t) → U
Polygon(U, T, W, V) → mangekant2, u, t_1, w, v
Rotate(U, ho, O) → U'
Rotate(T, ho, O) → T'
Polygon(U', T', W', V') → mangekant2', u', t', w', v'
OrthogonalLine(T', q) → c_1
OrthogonalLine(W', q) → d_1
OrthogonalLine(V', q) → e_1
OrthogonalLine(U', q) → f_1
OrthogonalLine(T', q) → g_1
OrthogonalLine(U', q) → k_1
Intersect(g_1, q) → Z
Intersect(q, k_1) → B_1
Distance(Z, T') → avstandZT'
Distance(B_1, U') → avstandB1U'
Dilate(T', l1, Z) → T''
Dilate(U', l1, B_1) → U''
Polygon(T'', W'', V'', U'') → mangekant3, t'', w'', v'', u''
Midpoint(V'', U'') → E_1
Distance(O, E_1) → avstandOE1
Dilate(D_1, ix, O) → F_1
If((0 < ho) ∧ (ho < π) ∧ ((-π) / 2 < ve) ∧ (ve < π / 2) ∨ (-π < ho) ∧ (ho < 0) ∧ ((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)), van / (size - yp) + 3, (-van) / (size - yp) - 3) → iy
Dilate(E_1, iy, O) → G_1
Circle(O, size) → p_1
Circle(O, zp) → q_1
Intersect(q_1, p) → J_1, K_1
Dilate(K_1, iz, O) → H_1
Dilate(D_1, xpos, O) → I_1
Dilate(D_1, xneg, O) → L_1
Dilate(E_1, ypos, O) → M_1
Dilate(E_1, yneg, O) → N_1
Line(M_1, F_1) → m_1
Line(N_1, F_1) → n_1
Line(L_1, G_1) → r_1
Line(I_1, G_1) → s_1
Intersect(n_1, r_1) → O_1
Intersect(m_1, r_1) → P_1
Intersect(s_1, m_1) → Q_1
Intersect(s_1, n_1) → R_1
Polygon(P_1, O_1, R_1, Q_1) → mangekant4, p_2, o_1, r_2, q_2
Dilate(K_1, zpos, O) → S_1
Dilate(K_1, zneg, O) → T_1
Segment(I_1, L_1) → a_2
Segment(N_1, M_1) → b_2
Line(F_1, S_1) → c_2
Line(T_1, F_1) → d_2
Line(S_1, G_1) → e_2
Line(T_1, G_1) → f_2
Line(H_1, N_1) → g_2
Line(H_1, I_1) → h_2
Line(H_1, L_1) → i_2
Line(H_1, M_1) → j_2
Intersect(g_2, e_2) → V_1
Intersect(g_2, f_2) → W_1
Intersect(e_2, j_2) → Z_1
Intersect(f_2, j_2) → A_2
Line(V_1, F_1) → k_2
Line(Z_1, F_1) → l_2
Line(W_1, F_1) → m_2
Line(A_2, F_1) → n_2
Intersect(i_2, c_2) → B_2
Intersect(i_2, d_2) → C_2
Intersect(c_2, h_2) → D_2
Intersect(h_2, d_2) → E_2
Line(B_2, G_1) → s_2
Line(D_2, G_1) → t_2
Line(E_2, G_1) → a_3
Line(C_2, G_1) → b_3
Intersect(k_2, s_2) → F_2
Intersect(s_2, l_2) → G_2
Intersect(t_2, l_2) → H_2
Intersect(t_2, k_2) → I_2
Intersect(m_2, b_3) → J_2
Intersect(m_2, a_3) → K_2
Intersect(a_3, n_2) → L_2
Intersect(n_2, b_3) → M_2
Segment(F_2, G_2) → c_3
Segment(G_2, H_2) → d_3
Segment(H_2, I_2) → e_3
Segment(I_2, F_2) → f_3
Segment(F_2, J_2) → g_3
Segment(I_2, K_2) → h_3
Segment(L_2, H_2) → i_3
Segment(G_2, M_2) → j_3
Segment(M_2, L_2) → k_3
Segment(L_2, K_2) → l_3
Segment(K_2, J_2) → m_3
Segment(J_2, M_2) → n_3
Segment(T_1, S_1) → p_3
Dilate(I_1, enx, O) → N_2
Dilate(I_1, tox, O) → O_2
Dilate(I_1, trex, O) → P_2
Dilate(I_1, fix, O) → Q_2
Dilate(I_1, fex, O) → R_2
Dilate(I_1, enxm, O) → S_2
Dilate(I_1, six, O) → T_2
Dilate(I_1, sevx, O) → U_2
Dilate(I_1, eix, O) → V_2
Dilate(I_1, nix, O) → W_2
Dilate(I_1, tex, O) → Z_2
Dilate(I_1, toxm, O) → A_3
Dilate(I_1, trexm, O) → B_3
Dilate(I_1, fixm, O) → C_3
Dilate(I_1, fexm, O) → D_3
Dilate(I_1, sixm, O) → E_3
Dilate(I_1, sevxm, O) → F_3
Dilate(I_1, eixm, O) → G_3
Dilate(I_1, nixm, O) → H_3
Dilate(I_1, texm, O) → I_3
Line(Z_2, G_1) → q_3
Line(W_2, G_1) → r_3
Line(V_2, G_1) → s_3
Line(U_2, G_1) → t_3
Line(T_2, G_1) → a_4
Line(R_2, G_1) → b_4
Line(Q_2, G_1) → c_4
Line(P_2, G_1) → d_4
Line(O_2, G_1) → e_4
Line(N_2, G_1) → f_4
Line(S_2, G_1) → g_4
Line(A_3, G_1) → h_4
Line(B_3, G_1) → i_4
Line(C_3, G_1) → j_4
Line(D_3, G_1) → k_4
Line(E_3, G_1) → l_4
Line(F_3, G_1) → m_4
Line(G_3, G_1) → n_4
Line(H_3, G_1) → p_4
Line(I_3, G_1) → q_4
Intersect(q_2, q_4) → J_3
Intersect(q_2, p_4) → K_3
Intersect(q_2, n_4) → L_3
Intersect(q_2, m_4) → M_3
Intersect(q_2, l_4) → N_3
Intersect(q_2, k_4) → O_3
Intersect(q_2, j_4) → P_3
Intersect(q_2, i_4) → Q_3
Intersect(q_2, h_4) → R_3
Intersect(q_2, g_4) → S_3
Intersect(q_2, f_4) → T_3
Intersect(q_2, e_4) → U_3
Intersect(q_2, d_4) → V_3
Intersect(q_2, c_4) → W_3
Intersect(q_2, b_4) → Z_3
Intersect(q_2, a_4) → A_4
Intersect(q_2, t_3) → B_4
Intersect(q_2, s_3) → C_4
Intersect(q_2, r_3) → D_4
Intersect(q_2, q_3) → E_4
Intersect(o_1, q_3) → F_4
Intersect(o_1, r_3) → G_4
Intersect(o_1, s_3) → H_4
Intersect(o_1, t_3) → I_4
Intersect(o_1, a_4) → J_4
Intersect(o_1, b_4) → K_4
Intersect(o_1, c_4) → L_4
Intersect(o_1, d_4) → M_4
Intersect(o_1, e_4) → N_4
Intersect(o_1, f_4) → O_4
Intersect(o_1, g_4) → P_4
Intersect(o_1, h_4) → Q_4
Intersect(o_1, i_4) → R_4
Intersect(o_1, j_4) → S_4
Intersect(o_1, k_4) → T_4
Intersect(o_1, m_4) → W_4
Intersect(o_1, n_4) → Z_4
Intersect(o_1, p_4) → A_5
Intersect(o_1, q_4) → B_5
Segment(B_5, J_3) → r_4
Segment(A_5, K_3) → s_4
Segment(Z_4, L_3) → t_4
Segment(W_4, M_3) → a_5
Segment(T_4, O_3) → c_5
Segment(S_4, P_3) → d_5
Segment(R_4, Q_3) → e_5
Segment(Q_4, R_3) → f_5
Segment(P_4, S_3) → g_5
Segment(O_4, T_3) → h_5
Segment(N_4, U_3) → i_5
Segment(M_4, V_3) → j_5
Segment(L_4, W_3) → k_5
Segment(K_4, Z_3) → l_5
Segment(J_4, A_4) → m_5
Segment(I_4, B_4) → n_5
Segment(H_4, C_4) → p_5
Segment(G_4, D_4) → q_5
Segment(F_4, E_4) → r_5
Dilate(M_1, eny, O) → C_5
Dilate(M_1, toy, O) → D_5
Dilate(M_1, trey, O) → E_5
Dilate(M_1, firy, O) → F_5
Dilate(M_1, femy, O) → G_5
Dilate(M_1, sixy, O) → H_5
Dilate(M_1, sevy, O) → I_5
Dilate(M_1, eiy, O) → J_5
Dilate(M_1, niy, O) → K_5
Dilate(M_1, tey, O) → L_5
Dilate(M_1, toym, O) → M_5
Dilate(M_1, enym, O) → N_5
Dilate(M_1, treym, O) → O_5
Dilate(M_1, firym, O) → P_5
Dilate(M_1, sixym, O) → Q_5
Dilate(M_1, femym, O) → R_5
Dilate(M_1, sevym, O) → S_5
Dilate(M_1, eiym, O) → T_5
Dilate(M_1, niym, O) → U_5
Dilate(M_1, teym, O) → V_5
Line(V_5, F_1) → s_5
Line(U_5, F_1) → t_5
Line(T_5, F_1) → a_6
Line(S_5, F_1) → b_6
Line(Q_5, F_1) → c_6
Line(R_5, F_1) → d_6
Line(P_5, F_1) → e_6
Line(O_5, F_1) → f_6
Line(M_5, F_1) → g_6
Line(N_5, F_1) → h_6
Line(C_5, F_1) → i_6
Line(D_5, F_1) → j_6
Line(E_5, F_1) → k_6
Line(F_5, F_1) → l_6
Line(G_5, F_1) → m_6
Line(H_5, F_1) → n_6
Line(I_5, F_1) → p_6
Line(J_5, F_1) → q_6
Line(K_5, F_1) → r_6
Line(L_5, F_1) → s_6
Intersect(p_2, s_5) → W_5
Intersect(p_2, t_5) → Z_5
Intersect(p_2, a_6) → A_6
Intersect(p_2, b_6) → B_6
Intersect(p_2, c_6) → C_6
Intersect(p_2, d_6) → D_6
Intersect(p_2, e_6) → E_6
Intersect(p_2, f_6) → F_6
Intersect(p_2, g_6) → G_6
Intersect(p_2, h_6) → H_6
Intersect(p_2, i_6) → I_6
Intersect(p_2, j_6) → J_6
Intersect(p_2, k_6) → K_6
Intersect(p_2, l_6) → L_6
Intersect(p_2, m_6) → M_6
Intersect(p_2, n_6) → N_6
Intersect(p_2, p_6) → O_6
Intersect(p_2, q_6) → P_6
Intersect(p_2, r_6) → Q_6
Intersect(p_2, s_6) → R_6
Intersect(r_2, s_6) → S_6
Intersect(r_2, r_6) → T_6
Intersect(r_2, q_6) → U_6
Intersect(r_2, p_6) → V_6
Intersect(r_2, n_6) → W_6
Intersect(r_2, m_6) → Z_6
Intersect(r_2, l_6) → A_7
Intersect(r_2, k_6) → B_7
Intersect(r_2, j_6) → C_7
Intersect(r_2, i_6) → D_7
Intersect(r_2, h_6) → E_7
Intersect(r_2, g_6) → F_7
Intersect(r_2, f_6) → G_7
Intersect(r_2, e_6) → H_7
Intersect(r_2, d_6) → I_7
Intersect(r_2, c_6) → J_7
Intersect(r_2, b_6) → K_7
Intersect(r_2, a_6) → L_7
Intersect(r_2, t_5) → M_7
Intersect(r_2, s_5) → N_7
Segment(N_7, W_5) → t_6
Segment(M_7, Z_5) → a_7
Segment(L_7, A_6) → b_7
Segment(K_7, B_6) → c_7
Segment(J_7, C_6) → d_7
Segment(I_7, D_6) → e_7
Segment(H_7, E_6) → f_7
Segment(G_7, F_6) → g_7
Segment(F_7, G_6) → h_7
Segment(E_7, H_6) → i_7
Segment(D_7, I_6) → j_7
Segment(C_7, J_6) → k_7
Segment(B_7, K_6) → l_7
Segment(A_7, L_6) → m_7
Segment(Z_6, M_6) → n_7
Segment(W_6, N_6) → p_7
Segment(V_6, O_6) → q_7
Segment(U_6, P_6) → r_7
Segment(T_6, Q_6) → s_7
Segment(S_6, R_6) → t_7
Intersect(o_1, l_4) → U_4
Intersect(q_2, l_4) → V_4
Segment(U_4, V_4) → b_5
Dilate(S_1, enz, O) → O_7
Vector(O, N_2) → z
Vector(O, C_5) → u_1
Vector(O, O_7) → v_1
Textfield(x1) → inputBox1
Dilate(I_1, xx1, O) → A
Textfield(y1) → inputBox2
Dilate(M_1, yy1, O) → B
Textfield(z1) → inputBox3
Dilate(S_1, zz1, O) → C
Line(H_1, A) → a_8
Line(H_1, B) → b_8
Line(C, G_1) → c_8
Line(A, G_1) → d_8
Line(C, F_1) → e_8
Line(B, F_1) → f_8
Intersect(b_8, c_8) → P_7
Intersect(a_8, e_8) → Q_7
Line(P_7, F_1) → g_8
Line(Q_7, G_1) → h_8
Intersect(g_8, h_8) → P1
Intersect(f_8, d_8) → S_7
Segment(A, S_7) → i_8
Segment(S_7, B) → j_8
Segment(S_7, P1) → k_8
Segment(P1, C) → l_8
Dilate(I_1, xx2, O) → R_7
Dilate(M_1, yy2, O) → T_7
Dilate(S_1, zz2, O) → U_7
Textfield(x2) → inputBox4
Textfield(y2) → inputBox5
Textfield(z2) → inputBox6
Line(H_1, R_7) → m_8
Line(H_1, T_7) → n_8
Line(U_7, G_1) → p_8
Line(R_7, G_1) → q_8
Line(U_7, F_1) → r_8
Line(T_7, F_1) → s_8
Intersect(n_8, p_8) → V_7
Intersect(m_8, r_8) → W_7
Line(V_7, F_1) → t_8
Line(W_7, G_1) → a_9
Intersect(t_8, a_9) → P2
Intersect(s_8, q_8) → A_8
Segment(R_7, A_8) → b_9
Segment(A_8, T_7) → c_9
Segment(A_8, P2) → d_9
Segment(P2, U_7) → e_9
Dilate(I_1, xx3, O) → Z_7
Dilate(M_1, yy3, O) → B_8
Dilate(S_1, zz3, O) → C_8
Textfield(x3) → inputBox7
Textfield(y3) → inputBox8
Textfield(z3) → inputBox9
Line(H_1, Z_7) → f_9
Line(H_1, B_8) → g_9
Line(B_8, F_1) → h_9
Line(C_8, F_1) → i_9
Line(C_8, G_1) → j_9
Line(Z_7, G_1) → k_9
Intersect(f_9, i_9) → D_8
Intersect(g_9, j_9) → E_8
Line(D_8, G_1) → l_9
Line(E_8, F_1) → m_9
Intersect(l_9, m_9) → P3
Intersect(k_9, h_9) → G_8
Segment(G_8, B_8) → n_9
Segment(G_8, Z_7) → p_9
Segment(G_8, P3) → q_9
Segment(P3, C_8) → r_9
Segment(P1, P2) → s_9
Segment(P1, P3) → t_9
Segment(P3, P2) → a_{10}
Dilate(I_1, xx4, O) → F_8
Dilate(M_1, yy4, O) → H_8
Dilate(S_1, zz4, O) → I_8
Textfield(x4) → inputBox10
Textfield(y4) → inputBox11
Textfield(z4) → inputBox12
Line(H_1, F_8) → b_{10}
Line(H_1, H_8) → c_{10}
Line(F_8, G_1) → d_{10}
Line(I_8, G_1) → e_{10}
Line(I_8, F_1) → f_{10}
Line(H_8, F_1) → g_{10}
Intersect(b_{10}, f_{10}) → J_8
Intersect(c_{10}, e_{10}) → K_8
Line(K_8, F_1) → h_{10}
Line(J_8, G_1) → i_{10}
Intersect(h_{10}, i_{10}) → P4
Intersect(g_{10}, d_{10}) → M_8
Segment(M_8, H_8) → j_{10}
Segment(M_8, F_8) → k_{10}
Segment(M_8, P4) → l_{10}
Segment(P4, I_8) → m_{10}
Segment(P1, P4) → n_{10}
Segment(P3, P4) → p_{10}
Segment(P2, P4) → q_{10}
Dilate(I_1, xx5, O) → L_8
Dilate(M_1, yy5, O) → N_8
Dilate(S_1, zz5, O) → O_8
Line(H_1, L_8) → r_{10}
Line(H_1, N_8) → s_{10}
Line(L_8, G_1) → t_{10}
Line(O_8, G_1) → a_{11}
Line(O_8, F_1) → b_{11}
Line(N_8, F_1) → c_{11}
Intersect(r_{10}, b_{11}) → P_8
Intersect(s_{10}, a_{11}) → Q_8
Line(Q_8, F_1) → d_{11}
Line(P_8, G_1) → e_{11}
Intersect(d_{11}, e_{11}) → P5
Intersect(c_{11}, t_{10}) → S_8
Segment(L_8, S_8) → f_{11}
Segment(S_8, N_8) → g_{11}
Segment(S_8, P5) → h_{11}
Segment(P5, O_8) → i_{11}
Textfield(x5) → inputBox13
Textfield(y5) → inputBox14
Textfield(z5) → inputBox15
Segment(P1, P5) → j_{11}
Segment(P2, P5) → k_{11}
Segment(P3, P5) → l_{11}
Segment(P4, P5) → m_{11}
Polygon(P1, P2, P5) → poly3, p5, p1_2, p2_2
Polygon(P1, P3, P4) → poly4, p4_1, p1_3, p3_1
Polygon(P1, P3, P5) → poly5, p5_1, p1_4, p3_2
Polygon(P1, P4, P5) → poly6, p5_2, p1_5, p4_2
Polygon(P2, P3, P4) → poly7, p4_3, p2_3, p3_3
Polygon(P2, P3, P5) → poly8, p5_3, p2_4, p3_4
Polygon(P2, P4, P5) → poly9, p5_4, p2_5, p4_4
Polygon(P3, P4, P5) → poly10, p5_5, p3_5, p4_5
Dilate(I_1, lex1, O) → L
Dilate(M_1, ley1, O) → R_8
Dilate(S_1, lez1, O) → T_8
Line(H_1, R_8) → n_{11}
Line(H_1, L) → p_{11}
Line(L, G_1) → q_{11}
Line(T_8, G_1) → r_{11}
Line(T_8, F_1) → s_{11}
Line(R_8, F_1) → t_{11}
Intersect(n_{11}, r_{11}) → U_8
Intersect(p_{11}, s_{11}) → V_8
Line(U_8, F_1) → a_{12}
Line(V_8, G_1) → b_{12}
Intersect(a_{12}, b_{12}) → W_8
Intersect(t_{11}, q_{11}) → Z_8
Segment(R_8, Z_8) → c_{12}
Segment(Z_8, L) → d_{12}
Segment(Z_8, W_8) → e_{12}
Segment(W_8, T_8) → g_{12}
Dilate(I_1, lex2, O) → A_9
Dilate(M_1, ley2, O) → B_9
Dilate(S_1, lez2, O) → C_9
Line(H_1, B_9) → h_{12}
Line(H_1, A_9) → i_{12}
Line(C_9, G_1) → j_{12}
Line(A_9, G_1) → k_{12}
Line(C_9, F_1) → l_{12}
Line(B_9, F_1) → m_{12}
Intersect(h_{12}, j_{12}) → D_9
Intersect(i_{12}, l_{12}) → E_9
Line(D_9, F_1) → n_{12}
Line(E_9, G_1) → p_{12}
Intersect(n_{12}, p_{12}) → F_9
Intersect(k_{12}, m_{12}) → G_9
Segment(G_9, B_9) → q_{12}
Segment(G_9, A_9) → r_{12}
Segment(G_9, F_9) → s_{12}
Segment(F_9, C_9) → t_{12}
Segment(P1, F_9) → a_{13}
Segment(P2, W_8) → b_{13}
Dilate(I_1, nx11, O) → H_9
Dilate(M_1, ny11, O) → I_9
Dilate(S_1, nz11, O) → J_9
Line(H_1, I_9) → c_{13}
Line(H_1, H_9) → d_{13}
Line(I_9, F_1) → e_{13}
Line(J_9, F_1) → f_{13}
Line(J_9, G_1) → g_{13}
Line(H_9, G_1) → h_{13}
Intersect(c_{13}, g_{13}) → K_9
Intersect(d_{13}, f_{13}) → L_9
Line(L_9, G_1) → i_{13}
Line(K_9, F_1) → j_{13}
Intersect(i_{13}, j_{13}) → M_9
Vector(P1, M_9) → w_6
Dilate(I_1, nx22, O) → N_9
Dilate(M_1, ny22, O) → O_9
Dilate(S_1, nz22, O) → P_9
Line(H_1, N_9) → k_{13}
Line(H_1, O_9) → l_{13}
Line(P_9, G_1) → m_{13}
Line(N_9, G_1) → n_{13}
Line(P_9, F_1) → p_{13}
Line(O_9, F_1) → q_{13}
Intersect(k_{13}, p_{13}) → Q_9
Intersect(l_{13}, m_{13}) → R_9
Line(R_9, F_1) → r_{13}
Line(Q_9, G_1) → s_{13}
Intersect(r_{13}, s_{13}) → S_9
Vector(P1, S_9) → u_7
Dilate(I_1, shp3x, O) → T_9
Dilate(M_1, shp3y, O) → U_9
Dilate(S_1, shp3z, O) → V_9
Line(H_1, U_9) → t_{13}
Line(H_1, T_9) → a_{14}
Line(V_9, G_1) → b_{14}
Line(T_9, G_1) → c_{14}
Line(V_9, F_1) → d_{14}
Line(U_9, F_1) → e_{14}
Intersect(t_{13}, b_{14}) → W_9
Intersect(a_{14}, d_{14}) → Z_9
Line(W_9, F_1) → f_{14}
Line(Z_9, G_1) → g_{14}
Intersect(f_{14}, g_{14}) → A_{10}
Dilate(I_1, shp4x, O) → B_{10}
Dilate(M_1, shp4y, O) → C_{10}
Dilate(S_1, shp4z, O) → D_{10}
Line(H_1, B_{10}) → h_{14}
Line(H_1, C_{10}) → i_{14}
Line(D_{10}, G_1) → j_{14}
Line(B_{10}, G_1) → k_{14}
Line(D_{10}, F_1) → l_{14}
Line(C_{10}, F_1) → m_{14}
Intersect(h_{14}, l_{14}) → E_{10}
Intersect(i_{14}, j_{14}) → F_{10}
Line(F_{10}, F_1) → n_{14}
Line(E_{10}, G_1) → p_{14}
Intersect(n_{14}, p_{14}) → G_{10}
Dilate(I_1, shp3x1, O) → H_{10}
Dilate(M_1, shp3y1, O) → I_{10}
Dilate(S_1, shp3z1, O) → J_{10}
Line(H_1, H_{10}) → q_{14}
Line(H_1, I_{10}) → r_{14}
Line(C, G_1) → s_{14}
Line(H_{10}, G_1) → t_{14}
Line(C, F_1) → a_{15}
Line(I_{10}, F_1) → b_{15}
Intersect(q_{14}, a_{15}) → K_{10}
Intersect(r_{14}, s_{14}) → L_{10}
Line(L_{10}, F_1) → c_{15}
Line(K_{10}, G_1) → d_{15}
Dilate(I_1, shp3x2, O) → N_{10}
Dilate(M_1, shp3y2, O) → O_{10}
Dilate(S_1, shp3z2, O) → P_{10}
Line(H_1, O_{10}) → e_{15}
Line(H_1, N_{10}) → f_{15}
Line(P_{10}, G_1) → g_{15}
Line(N_{10}, G_1) → h_{15}
Line(P_{10}, F_1) → i_{15}
Line(O_{10}, F_1) → j_{15}
Intersect(e_{15}, g_{15}) → Q_{10}
Intersect(f_{15}, i_{15}) → R_{10}
Line(Q_{10}, F_1) → k_{15}
Line(R_{10}, G_1) → l_{15}
Intersect(k_{15}, l_{15}) → S_{10}
Dilate(I_1, shp3x1, O) → M_{10}
Dilate(M_1, shp3y1, O) → T_{10}
Dilate(S_1, shp3z1, O) → U_{10}
Line(H_1, M_{10}) → m_{15}
Line(H_1, T_{10}) → n_{15}
Line(M_{10}, G_1) → p_{15}
Line(U_{10}, G_1) → q_{15}
Line(T_{10}, F_1) → r_{15}
Line(U_{10}, F_1) → s_{15}
Intersect(m_{15}, s_{15}) → V_{10}
Intersect(n_{15}, q_{15}) → W_{10}
Line(W_{10}, F_1) → t_{15}
Line(V_{10}, G_1) → a_{16}
Intersect(t_{15}, a_{16}) → Z_{10}
Dilate(I_1, shp3x3, O) → A_{11}
Dilate(M_1, shp3y3, O) → B_{11}
Dilate(S_1, shp3z3, O) → C_{11}
Line(H_1, A_{11}) → b_{16}
Line(H_1, B_{11}) → c_{16}
Line(C_{11}, G_1) → d_{16}
Line(A_{11}, G_1) → e_{16}
Line(C_{11}, F_1) → f_{16}
Line(B_{11}, F_1) → g_{16}
Intersect(c_{16}, d_{16}) → D_{11}
Intersect(b_{16}, f_{16}) → E_{11}
Line(D_{11}, F_1) → h_{16}
Line(E_{11}, G_1) → i_{16}
Intersect(h_{16}, i_{16}) → F_{11}
Polygon(A_{10}, S_{10}, F_{11}, Z_{10}) → poly11, a_{17}, s_{16}, f_{17}, z_{10}
Dilate(I_1, shp4x1, O) → G_{11}
Dilate(M_1, shp4y1, O) → H_{11}
Dilate(S_1, shp4z1, O) → I_{11}
Line(H_1, G_{11}) → j_{16}
Line(H_1, H_{11}) → k_{16}
Line(I_{11}, G_1) → l_{16}
Line(G_{11}, G_1) → m_{16}
Line(I_{11}, F_1) → n_{16}
Line(H_{11}, F_1) → p_{16}
Intersect(j_{16}, n_{16}) → J_{11}
Intersect(k_{16}, l_{16}) → K_{11}
Line(K_{11}, F_1) → q_{16}
Line(J_{11}, G_1) → r_{16}
Intersect(q_{16}, r_{16}) → L_{11}
Dilate(I_1, shp4x2, O) → M_{11}
Dilate(M_1, shp4y2, O) → N_{11}
Dilate(S_1, shp4z2, O) → O_{11}
Line(H_1, M_{11}) → t_{16}
Line(H_1, N_{11}) → b_{17}
Line(O_{11}, G_1) → c_{17}
Line(M_{11}, G_1) → d_{17}
Line(O_{11}, F_1) → e_{17}
Line(N_{11}, F_1) → g_{17}
Intersect(b_{17}, c_{17}) → P_{11}
Intersect(t_{16}, e_{17}) → Q_{11}
Line(P_{11}, F_1) → h_{17}
Line(Q_{11}, G_1) → i_{17}
Intersect(h_{17}, i_{17}) → R_{11}
Dilate(I_1, shp4x4, O) → S_{11}
Dilate(M_1, shp4y4, O) → T_{11}
Dilate(S_1, shp4z4, O) → U_{11}
Line(H_1, T_{11}) → j_{17}
Line(H_1, S_{11}) → k_{17}
Line(S_{11}, G_1) → l_{17}
Line(U_{11}, G_1) → m_{17}
Line(U_{11}, F_1) → n_{17}
Line(T_{11}, F_1) → p_{17}
Intersect(j_{17}, m_{17}) → V_{11}
Intersect(k_{17}, n_{17}) → W_{11}
Line(V_{11}, F_1) → q_{17}
Line(W_{11}, G_1) → r_{17}
Intersect(q_{17}, r_{17}) → Z_{11}
Polygon(Z_{11}, L_{11}, G_{10}, R_{11}) → poly1, z_{11}, l_{18}, g_{18}, r_{18}
Polygon(P1, P2, P3) → poly2, p3, p1, p2
Polygon(P1, P4, P2) → poly12, p2_1, p1_1, p4

AI Drawing Prompt Reference

Draw a 3D geometric diagram with two concentric circles as bases. Through the common center, draw an inclined line and a perpendicular line intersecting both circles at several points. From these points, construct perpendicular lines to form two sets of parallel lines, which intersect to create a rectangular pyramid base. On the other side, use a smaller circle, draw a perpendicular through its center to meet the circle at two points, then construct perpendiculars from these points to intersect, giving two points. Rotate these points around the center by an angle, then dilate them along the perpendicular direction to obtain two new points, and take their midpoint. Finally, connect the two sets of points to form two quadrilaterals, illustrating spatial relationships among points, lines, and planes.

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