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Perspective Cube

Perspective Cube
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2019-03-08 06:49
VectorSolid GeometryGeometric Construction
In collections SPATIAL VISUALISATION TASKS
This example demonstrates the geometric construction of a perspective cube. It involves basic concepts of solid geometry such as the faces, edges, and vertices of a cube. Using GeoGebra commands like Intersect, Point, Cube, Vector, and Translate, it dynamically showcases the various faces and edges of the cube. Suitable for middle and high school students learning 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) → k, D, stenaCDHG, stenaEFGH, hranaAD, hranaAB, hranaBC, hranaCD, hranaAE, hranaDH, hranaEH, hranaEF, E, hranaBF, hranaFG, hranaCG, hranaGH, F, G, H, stenaABCD, stenaADHE, stenaABFE, stenaBCGF
  5. Intersect(hranaDH, hranaAD) → M_1
  6. Intersect(hranaFG, hranaBF) → L_1
  7. Vector(L_1, M_1) → u_1
  8. Intersect(hranaAB, hranaAD) → I
  9. Intersect(hranaAB, hranaBC) → J
  10. Vector(I, J) → u
  11. Intersect(hranaAD, hranaCD) → K
  12. Vector(I, K) → v
  13. Intersect(zAxis, hranaEH) → L
  14. Vector(I, L) → w
  15. Intersect(xAxis, hranaBC) → J_1
  16. Intersect(hranaEH, hranaAE) → G_1
  17. Vector(J_1, G_1) → c
  18. Intersect(yAxis, zAxis) → H_1
  19. Intersect(hranaFG, hranaBF) → E_1
  20. Vector(H_1, E_1) → t
  21. Intersect(hranaFG, hranaGH) → I_1
  22. Vector(G_1, I_1) → s
  23. Intersect(hranaGH, hranaDH) → K_1
  24. Vector(E_1, K_1) → r
  25. Vector(J_1, I_1) → q
  26. Intersect(hranaCG, hranaCD) → F_1
  27. Vector(F_1, E_1) → n
  28. Vector(H_1, I_1) → m
  29. Vector(F_1, G_1) → j
  30. Intersect(hranaCD, hranaAD) → D_1
  31. Vector(D_1, E_1) → i
  32. Intersect(hranaFG, hranaGH) → A_1
  33. Intersect(hranaBF, hranaAB) → Z
  34. Vector(Z, A_1) → c_1
  35. Point(hranaGH) → C_1
  36. Intersect(hranaBF, hranaAB) → B_1
  37. Vector(B_1, C_1) → e
  38. Point(zAxis) → S
  39. Intersect(xAxis, zAxis) → Q
  40. Vector(Q, S) → d
  41. Point(zAxis) → R
  42. Vector(Q, R) → h
  43. Point(xAxis) → V
  44. Point(xAxis) → U
  45. Vector(U, V) → g
  46. Point(xAxis) → T
  47. Vector(Q, T) → f
  48. Intersect(hranaCG, hranaBC) → M
  49. Intersect(hranaFG, hranaGH) → N
  50. Point(zAxis) → O
  51. Point(yAxis) → P
  52. Vector(I, P) → l
  53. Vector(J, M) → p
  54. Translate(k, Vector[(-2 * v) - (2 * u) - (2 * w) + (a * (-m))]) → k'
  55. Translate(k, Vector[(-v) - (2 * u) - (2 * w) + (a * (-t))]) → k'_1
  56. Translate(k, Vector[v - (2 * u) - (2 * w) + (a * (-t))]) → k'_3
  57. Translate(k, Vector[(-2 * u) - (2 * w) + (a * (-t))]) → k'_2
  58. Translate(k, Vector[(2 * v) - (2 * u) - (2 * w) + (a * u_1)]) → k'_4
  59. Translate(k, Vector[(-2 * v) - (2 * u) - w + (a * (-s))]) → k'_5
  60. Translate(k, Vector[(-v) - (2 * u) - w + (a * g)]) → k'_6
  61. Translate(k, Vector[(2 * v) - (2 * u) - w + (a * r)]) → k'_9
  62. Translate(k, Vector[(-2 * u) - w + (a * g)]) → k'_7
  63. Translate(k, Vector[(-2 * u) + v - w + (a * g)]) → k'_8
  64. Translate(k, Vector[(-2 * u) - (2 * v) + (a * (-s))]) → k'_{10}
  65. Translate(k, Vector[(-2 * u) - v + (a * g)]) → k'_{11}
  66. Translate(k, Vector[(-2 * u) + (a * g)]) → k'_{12}
  67. Translate(k, Vector[(-2 * u) + v + (a * g)]) → k'_{13}
  68. Translate(k, Vector[(-2 * u) + (2 * v) + (a * r)]) → k'_{14}
  69. Translate(k, Vector[(-2 * u) + w - v + (a * g)]) → k'_{16}
  70. Translate(k, Vector[(-2 * u) + w - (2 * v) + (a * (-s))]) → k'_{15}
  71. Translate(k, Vector[(-2 * u) + w + (a * g)]) → k'_{17}
  72. Translate(k, Vector[(-2 * u) + w + v + (a * g)]) → k'_{18}
  73. Translate(k, Vector[(-2 * u) + w + (2 * v) + (a * r)]) → k'_{19}
  74. Translate(k, Vector[(-2 * u) + (2 * w) - (2 * v) + (a * j)]) → k'_{20}
  75. Translate(k, Vector[(-2 * u) + (2 * w) - v + (a * c)]) → k'_{21}
  76. Translate(k, Vector[(-2 * u) + (2 * w) + (a * c)]) → k'_{22}
  77. Translate(k, Vector[(-2 * u) + (2 * w) + v + (a * c)]) → k'_{23}
  78. Translate(k, Vector[(-2 * u) + (2 * w) + (2 * v) + (a * e)]) → k'_{24}
  79. Translate(k, Vector[(-u) - (2 * w) - (2 * v) + (a * (-q))]) → k'_{25}
  80. Translate(k, Vector[(-u) - (2 * w) - v + (a * d)]) → k'_{26}
  81. Translate(k, Vector[(-u) - (2 * w) + (a * d)]) → k'_{27}
  82. Translate(k, Vector[(-u) - (2 * w) + v + (a * d)]) → k'_{28}
  83. Translate(k, Vector[(-u) - (2 * w) + (2 * v) + (a * (-n))]) → k'_{29}
  84. Translate(k, Vector[(-u) - w - (2 * v) + (a * l)]) → k'_{30}
  85. Translate(k, Vector[(-u) - w - v + (b * (-m))]) → k'_{31}
  86. Translate(k, Vector[(-u) - w + (b * (-t))]) → k'_{32}
  87. Translate(k, Vector[(-u) - w + v + (b * (-i))]) → k'_{33}
  88. Translate(k, Vector[(-u) - w + (2 * v) + (a * p)]) → k'_{34}
  89. Translate(k, Vector[(-u) - (2 * v) + (a * l)]) → k'_{35}
  90. Translate(k, Vector[(-u) - v + (b * (-s))]) → k'_{36}
  91. Translate(k, Vector[(-u) + (b * g)]) → k'_{38}
  92. Translate(k, Vector[(-u) + v + (b * r)]) → k'_{39}
  93. Translate(k, Vector[(-u) + (2 * v) + (a * p)]) → k'_{40}
  94. Translate(k, Vector[(-u) - (2 * v) + w + (a * l)]) → k'_{41}
  95. Translate(k, Vector[(-u) - v + w + (b * j)]) → k'_{42}
  96. Translate(k, Vector[(-u) + w + (b * c)]) → k'_{43}
  97. Translate(k, Vector[(-u) + v + w + (b * e)]) → k'_{44}
  98. Translate(k, Vector[(-u) + (2 * v) + w + (a * p)]) → k'_{45}
  99. Translate(k, Vector[(-u) - (2 * v) + (2 * w) + (a * n)]) → k'_{46}
  100. Translate(k, Vector[(-u) - v + (2 * w) + (a * h)]) → k'_{47}
  101. Translate(k, Vector[(-u) + (2 * w) + (a * h)]) → k'_{48}
  102. Translate(k, Vector[(-u) + (2 * w) + v + (a * h)]) → k'_{49}
  103. Translate(k, Vector[(-u) + (2 * w) + (2 * v) + (a * q)]) → k'_{50}
  104. Translate(k, Vector[(-2 * w) - (2 * v) + (a * (-q))]) → k'_{51}
  105. Translate(k, Vector[(-2 * w) - v + (a * d)]) → k'_{52}
  106. Translate(k, Vector[(-2 * w) + (a * d)]) → k'_{53}
  107. Translate(k, Vector[(-2 * w) + v + (a * d)]) → k'_{54}
  108. Translate(k, Vector[(-2 * w) + (2 * v) + (a * (-n))]) → k'_{55}
  109. Translate(k, Vector[(-w) - (2 * v) + (a * l)]) → k'_{56}
  110. Translate(k, Vector[(-w) - v + (b * (-c_1))]) → k'_{57}
  111. Translate(k, Vector[(-w) + v + (b * (-n))]) → k'_{59}
  112. Translate(k, Vector[(-w) + (b * d)]) → k'_{60}
  113. Translate(k, Vector[(-w) + (2 * v) + (a * p)]) → k'_{61}
  114. Translate(k, Vector[(-2 * v) + (a * l)]) → k'_{62}
  115. Translate(k, Vector[(-v) + (b * l)]) → k'_{63}
  116. Translate(k, Vector[v + (b * p)]) → k'_{65}
  117. Translate(k, Vector[(2 * v) + (a * p)]) → k'_{66}
  118. Translate(k, Vector[w - (2 * v) + (a * l)]) → k'_{67}
  119. Translate(k, Vector[w - v + (b * n)]) → k'_{68}
  120. Translate(k, Vector[w + (b * h)]) → k'_{69}
  121. Translate(k, Vector[w + v + (b * c_1)]) → k'_{70}
  122. Translate(k, Vector[w + (2 * v) + (a * p)]) → k'_{71}
  123. Translate(k, Vector[(2 * w) - (2 * v) + (a * n)]) → k'_{72}
  124. Translate(k, Vector[(2 * w) - v + (a * h)]) → k'_{73}
  125. Translate(k, Vector[(2 * w) + (a * h)]) → k'_{74}
  126. Translate(k, Vector[(2 * w) + v + (a * h)]) → k'_{75}
  127. Translate(k, Vector[(2 * w) + (2 * v) + (a * q)]) → k'_{76}
  128. Translate(k, Vector[u - (2 * w) - v + (a * d)]) → k'_{78}
  129. Translate(k, Vector[u - (2 * w) - (2 * v) + (a * (-q))]) → k'_{77}
  130. Translate(k, Vector[u - (2 * w) + (a * d)]) → k'_{79}
  131. Translate(k, Vector[u - (2 * w) + v + (a * d)]) → k'_{80}
  132. Translate(k, Vector[u - (2 * w) + (2 * v) + (a * (-n))]) → k'_{81}
  133. Translate(k, Vector[u - w - (2 * v) + (a * l)]) → k'_{82}
  134. Translate(k, Vector[u - w - v + (b * (-e))]) → k'_{83}
  135. Translate(k, Vector[u - w + (b * (-c))]) → k'_{84}
  136. Translate(k, Vector[u - w + v + (b * (-j))]) → k'_{85}
  137. Translate(k, Vector[u - w + (2 * v) + (a * p)]) → k'_{86}
  138. Translate(k, Vector[u - (2 * v) + (a * l)]) → k'_{87}
  139. Translate(k, Vector[u - v + (b * (-r))]) → k'_{88}
  140. Translate(k, Vector[u + (b * f)]) → k'_{89}
  141. Translate(k, Vector[u + v + (b * s)]) → k'_{90}
  142. Translate(k, Vector[u + (2 * v) + (a * p)]) → k'_{91}
  143. Translate(k, Vector[u + w - (2 * v) + (a * l)]) → k'_{92}
  144. Translate(k, Vector[u + w - v + (b * i)]) → k'_{93}
  145. Translate(k, Vector[u + w + (b * t)]) → k'_{94}
  146. Translate(k, Vector[u + w + v + (b * m)]) → k'_{95}
  147. Translate(k, Vector[u + w + (2 * v) + (a * p)]) → k'_{96}
  148. Translate(k, Vector[u + (2 * w) - (2 * v) + (a * n)]) → k'_{97}
  149. Translate(k, Vector[u + (2 * w) - v + (a * h)]) → k'_{98}
  150. Translate(k, Vector[u + (2 * w) + (a * h)]) → k'_{99}
  151. Translate(k, Vector[u + (2 * w) + v + (a * h)]) → k'_{100}
  152. Translate(k, Vector[u + (2 * w) + (2 * v) + (a * q)]) → k'_{101}
  153. Translate(k, Vector[(2 * u) - (2 * w) - (2 * v) + (a * (-e))]) → k'_{102}
  154. Translate(k, Vector[(2 * u) - (2 * w) - v + (a * (-c))]) → k'_{103}
  155. Translate(k, Vector[(2 * u) - (2 * w) + (a * (-c))]) → k'_{104}
  156. Translate(k, Vector[(2 * u) - (2 * w) + v + (a * (-c))]) → k'_{105}
  157. Translate(k, Vector[(2 * u) - (2 * w) + (2 * v) + (a * (-j))]) → k'_{106}
  158. Translate(k, Vector[(2 * u) - w - (2 * v) + (a * (-r))]) → k'_{107}
  159. Translate(k, Vector[(2 * u) - w - v + (a * f)]) → k'_{108}
  160. Translate(k, Vector[(2 * u) - w + (a * f)]) → k'_{109}
  161. Translate(k, Vector[(2 * u) - w + v + (a * f)]) → k'_{110}
  162. Translate(k, Vector[(2 * u) - w + (2 * v) + (a * s)]) → k'_{111}
  163. Translate(k, Vector[(2 * u) - (2 * v) + (a * (-r))]) → k'_{112}
  164. Translate(k, Vector[(2 * u) - v + (a * f)]) → k'_{113}
  165. Translate(k, Vector[(2 * u) + (a * f)]) → k'_{114}
  166. Translate(k, Vector[(2 * u) + v + (a * f)]) → k'_{115}
  167. Translate(k, Vector[(2 * u) + (2 * v) + (a * s)]) → k'_{116}
  168. Translate(k, Vector[w + (2 * u) - v + (a * f)]) → k'_{118}
  169. Translate(k, Vector[w + (2 * u) - (2 * v) + (a * (-r))]) → k'_{117}
  170. Translate(k, Vector[w + (2 * u) + (a * f)]) → k'_{119}
  171. Translate(k, Vector[w + (2 * u) + v + (a * f)]) → k'_{120}
  172. Translate(k, Vector[w + (2 * u) + (2 * v) + (a * s)]) → k'_{121}
  173. Translate(k, Vector[(2 * w) + (2 * u) - (2 * v) + (a * i)]) → k'_{122}
  174. Translate(k, Vector[(2 * w) + (2 * u) - v + (a * t)]) → k'_{123}
  175. Translate(k, Vector[(2 * w) + (2 * u) + (a * t)]) → k'_{124}
  176. Translate(k, Vector[(2 * w) + (2 * u) + v + (a * t)]) → k'_{125}
  177. Translate(k, Vector[(2 * w) + (2 * u) + (2 * v) + (a * m)]) → k'_{126}
  178. Point(k'_{95}) → W

AI Drawing Prompt Reference

Draw a perspective cube with all its faces, edges, and vertices. Start by creating the coordinate axes, then use points and vectors to create the cube's faces, such as face ABCD and face ADHE. Next, find the intersection points of edges, like the intersection of edge AD and edge CD to get point K, and finally connect these points to form the edges, such as the line segment hranaAD between edge AD and edge BC.
The prompt above was compiled from the original drawing commands and is for reference only.