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Snub Dodecahedron by chris cambré

Snub Dodecahedron by chris cambré
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2017-11-21 15:52
VectorSolid GeometryGeometric Construction
In collections Solids, graphs and paths
This example demonstrates the construction of a snub dodecahedron, a non-regular polyhedron consisting of 12 regular pentagons and 20 equilateral triangles. The construction uses commands such as rotation, reflection, angle, and vector, showcasing transformation and construction techniques in solid geometry. Suitable for high school mathematics education and students learning solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_0
  2. Circle(A_0, 1 / ((2 * sin(36°)))) → c
  3. Intersect(c, xAxis, 2) → A
  4. Rotate(A, 72°, A_0) → B
  5. Mirror(B, xAxis) → C
  6. Angle(A, A_0, D) → α
  7. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → E
  8. Dodecahedron(A, B, E) → e, F, O, P, Q, R, S, T, U, V, 면ABEFG, 면AGKQL, G, 면ABHML, 면BEINH, 면EFJOI, 면FGKPJ, 면KPUVQ, 면LMRVQ, 면HMRSN, 면INSTO, 면JOTUP, 면RSTUV, H, 모서리AG, 모서리AB, 모서리BE, 모서리EF, 모서리FG, 모서리AL, 모서리GK, 모서리KQ, 모서리LQ, 모서리LM, I, 모서리HM, 모서리BH, 모서리HN, 모서리IN, 모서리EI, 모서리IO, 모서리JO, 모서리FJ, 모서리JP, 모서리KP, J, 모서리PU, 모서리UV, 모서리QV, 모서리RV, 모서리MR, 모서리RS, 모서리NS, 모서리ST, 모서리OT, 모서리TU, K, L, M, N
  9. Midpoint(A, T) → W
  10. Centroid(B1) → C1
  11. Centroid(B2) → C2
  12. Centroid(B3) → C3
  13. Centroid(B4) → C4
  14. Centroid(B5) → C5
  15. Centroid(B6) → C6
  16. Centroid(B7) → C7
  17. Centroid(B8) → C8
  18. Centroid(B9) → C9
  19. Centroid(B10) → C10
  20. Centroid(B11) → C11
  21. Centroid(B12) → C12
  22. Vector(C1, D1) → E1
  23. Vector(C2, D2) → E2
  24. Vector(C3, D3) → E3
  25. Vector(C4, D4) → E4
  26. Vector(C5, D5) → E5
  27. Vector(C6, D6) → E6
  28. Vector(C7, D7) → E7
  29. Vector(C8, D8) → E8
  30. Vector(C9, D9) → E9
  31. Vector(C10, D10) → E10
  32. Vector(C11, D11) → E11
  33. Vector(C12, D12) → E12
  34. Rotate(Translate[B1, Vector[(k * E1)]], (k * α), Line[W, C1]) → F1
  35. Rotate(Translate[B2, Vector[(k * E2)]], (k * α), Line[W, C2]) → F2
  36. Rotate(Translate[B3, Vector[(k * E3)]], (k * α), Line[W, C3]) → F3
  37. Rotate(Translate[B4, Vector[(k * E4)]], (k * α), Line[W, C4]) → F4
  38. Rotate(Translate[B5, Vector[(k * E5)]], (k * α), Line[W, C5]) → F5
  39. Rotate(Translate[B6, Vector[(k * E6)]], (k * α), Line[W, C6]) → F6
  40. Rotate(Translate[B7, Vector[(k * E7)]], (k * α), Line[W, C7]) → F7
  41. Rotate(Translate[B8, Vector[(k * E8)]], (k * α), Line[W, C8]) → F8
  42. Rotate(Translate[B9, Vector[(k * E9)]], (k * α), Line[W, C9]) → F9
  43. Rotate(Translate[B10, Vector[(k * E10)]], (k * α), Line[W, C10]) → F10
  44. Rotate(Translate[B11, Vector[(k * E11)]], (k * α), Line[W, C11]) → F11
  45. Rotate(Translate[B12, Vector[(k * E12)]], (k * α), Line[W, C12]) → F12
  46. Vertex(F1) → G1, H1, I1, J1, K1
  47. Vertex(F2) → G2, H2, I2, J2, K2
  48. Vertex(F3) → G3, H3, I3, J3, K3
  49. Vertex(F4) → G4, H4, I4, J4, K4
  50. Vertex(F5) → G5, H5, I5, J5, K5
  51. Vertex(F6) → G6, H6, I6, J6, K6
  52. Vertex(F7) → G7, H7, I7, J7, K7
  53. Vertex(F8) → G8, H8, I8, J8, K8
  54. Vertex(F9) → G9, H9, I9, J9, K9
  55. Vertex(F10) → G10, H10, I10, J10, K10
  56. Vertex(F11) → G11, H11, I11, J11, K11
  57. Vertex(F12) → G12, H12, I12, J12, K12
  58. Polygon(G12, J11, K12) → 다각형1, k12, g12, j11
  59. Polygon(K12, J11, I7) → 다각형2, i7, k12_1, j11_1
  60. Polygon(K12, I7, J7) → 다각형3, j7, k12_2, i7_1
  61. Polygon(K12, J7, J12) → 다각형4, j12, k12_3, j7_1
  62. Polygon(J12, J7, I8) → 다각형5, i8, j12_1, j7_2
  63. Polygon(J12, I8, J8) → 다각형6, j8, j12_2, i8_1
  64. Polygon(J12, J8, I12) → 다각형7, i12, j12_3, j8_1
  65. Polygon(I12, J8, I9) → 다각형8, i9, i12_1, j8_2
  66. Polygon(I12, I9, J9) → 다각형9, j9, i12_2, i9_1
  67. Polygon(I12, J9, H12) → 다각형10, h12, i12_3, j9_1
  68. Polygon(H12, J9, J10) → 다각형11, j10, h12_1, j9_2
  69. Polygon(H12, J10, K10) → 다각형12, k10, h12_2, j10_1
  70. Polygon(H12, K10, G12) → 다각형13, g12_1, h12_3, k10_1
  71. Polygon(G12, K10, I11) → 다각형14, i11, g12_2, k10_2
  72. Polygon(G12, I11, J11) → 다각형15, j11_2, g12_3, i11_1
  73. Polygon(J9, K9, J10) → 다각형16, j10_2, j9_3, k9
  74. Polygon(J10, K9, I10) → 다각형17, i10, j10_3, k9_1
  75. Polygon(K10, G10, I11) → 다각형18, i11_2, k10_3, g10
  76. Polygon(I11, G10, H11) → 다각형19, h11, i11_3, g10_1
  77. Polygon(J11, K11, I7) → 다각형20, i7_2, j11_3, k11
  78. Polygon(I7, K11, H7) → 다각형21, h7, i7_3, k11_1
  79. Polygon(J7, K7, I8) → 다각형22, i8_2, j7_3, k7
  80. Polygon(I8, K7, H8) → 다각형23, h8, i8_3, k7_1
  81. Polygon(J8, K8, I9) → 다각형24, i9_2, j8_3, k8
  82. Polygon(I9, K8, H9) → 다각형25, h9, i9_3, k8_1
  83. Polygon(K8, G8, J5) → 다각형26, j5, k8_2, g8
  84. Polygon(K8, J5, H9) → 다각형27, h9_1, k8_3, j5_1
  85. Polygon(H9, J5, K5) → 다각형28, k5, h9_2, j5_2
  86. Polygon(H9, K5, G9) → 다각형29, g9, h9_3, k5_1
  87. Polygon(K9, G9, J6) → 다각형30, j6, k9_2, g9_1
  88. Polygon(K9, J6, I10) → 다각형31, i10_1, k9_3, j6_1
  89. Polygon(I10, J6, K6) → 다각형32, k6, i10_2, j6_2
  90. Polygon(I10, K6, H10) → 다각형33, h10, i10_3, k6_1
  91. Polygon(H10, K6, J3) → 다각형34, j3, h10_1, k6_2
  92. Polygon(H10, J3, K3) → 다각형35, k3, h10_2, j3_1
  93. Polygon(G10, H10, K3) → 다각형36, k3_1, g10_2, h10_3
  94. Polygon(G10, K3, H11) → 다각형37, h11_1, g10_3, k3_2
  95. Polygon(H11, K3, G3) → 다각형38, g3, h11_2, k3_3
  96. Polygon(H11, G3, G11) → 다각형39, g11, h11_3, g3_1
  97. Polygon(K11, G11, J2) → 다각형40, j2, k11_2, g11_1
  98. Polygon(K11, J2, H7) → 다각형41, h7_1, k11_3, j2_1
  99. Polygon(H7, J2, K2) → 다각형42, k2, h7_2, j2_2
  100. Polygon(H7, K2, G7) → 다각형43, g7, h7_3, k2_1
  101. Polygon(G7, K2, I4) → 다각형44, i4, g7_1, k2_2
  102. Polygon(K7, G7, J4) → 다각형45, j4, k7_2, g7_2
  103. Polygon(G7, I4, J4) → 다각형46, j4_1, g7_3, i4_1
  104. Polygon(K7, J4, H8) → 다각형47, h8_1, k7_3, j4_2
  105. Polygon(H8, J4, K4) → 다각형48, k4, h8_2, j4_3
  106. Polygon(H8, K4, G8) → 다각형49, g8_1, h8_3, k4_1
  107. Polygon(G8, K4, I5) → 다각형50, i5, g8_2, k4_2
  108. Polygon(G8, I5, J5) → 다각형51, j5_3, g8_3, i5_1
  109. Polygon(K4, G4, I5) → 다각형52, i5_2, k4_3, g4
  110. Polygon(I5, G4, H5) → 다각형53, h5, i5_3, g4_1
  111. Polygon(K2, G2, I4) → 다각형54, i4_2, k2_3, g2
  112. Polygon(I4, G2, H4) → 다각형55, h4, i4_3, g2_1
  113. Polygon(G11, G3, I2) → 다각형56, i2, g11_2, g3_2
  114. Polygon(G11, I2, J2) → 다각형57, j2_3, g11_3, i2_1
  115. Polygon(G3, H3, I2) → 다각형58, i2_2, g3_3, h3
  116. Polygon(I2, H3, H2) → 다각형59, h2, i2_3, h3_1
  117. Polygon(K6, G6, J3) → 다각형60, j3_2, k6_3, g6
  118. Polygon(J3, G6, I3) → 다각형61, i3, j3_3, g6_1
  119. Polygon(G9, K5, I6) → 다각형62, i6, g9_2, k5_2
  120. Polygon(G9, I6, J6) → 다각형63, j6_3, g9_3, i6_1
  121. Polygon(K5, G5, I6) → 다각형64, i6_2, k5_3, g5
  122. Polygon(I6, G5, H6) → 다각형65, h6, i6_3, g5_1
  123. Polygon(H5, K1, G5) → 다각형66, g5_2, h5_1, k1
  124. Polygon(G5, K1, H6) → 다각형67, h6_1, g5_3, k1_1
  125. Polygon(H6, K1, G1) → 다각형68, g1, h6_2, k1_2
  126. Polygon(H6, G1, G6) → 다각형69, g6_2, h6_3, g1_1
  127. Polygon(G6, G1, I3) → 다각형70, i3_1, g6_3, g1_2
  128. Polygon(G1, H1, I3) → 다각형71, i3_2, g1_3, h1
  129. Polygon(I3, H1, H3) → 다각형72, h3_2, i3_3, h1_1
  130. Polygon(H1, H2, H3) → 다각형73, h3_3, h1_2, h2_1
  131. Polygon(H5, J1, K1) → 다각형74, k1_3, h5_2, j1
  132. Polygon(H5, G4, J1) → 다각형75, j1_1, h5_3, g4_2
  133. Polygon(G4, H4, J1) → 다각형76, j1_2, g4_3, h4_1
  134. Polygon(J1, H4, I1) → 다각형77, i1, j1_3, h4_2
  135. Polygon(H4, G2, I1) → 다각형78, i1_1, h4_3, g2_2
  136. Polygon(G2, I1, H2) → 다각형79, h2_2, g2_3, i1_2
  137. Polygon(I1, H2, H1) → 다각형80, h1_3, i1_3, h2_3