Regular Polygon Prism with Net

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2016-05-10 19:56

In collections Surface Area and Volume Surface Area and Volume Surface Area and Volume

This example demonstrates the geometric construction of a regular polygon prism and its net. Key math concepts include polygons, prisms, nets, incircles, and geometric transformations. The construction uses commands like Point, Segment, Polygon, Prism, and Net, as outlined in the summary. Suitable for high school solid geometry instruction or geometric construction practice, helping students understand the relationship between spatial and planar figures.

GeoGebra Commands & Parameters

Point(Circle[A, s]) → B
Segment(A, B) → f
Polygon(A, B, n) → poly1, g, r, C, D, E, F, G, H, Q, S, p, i, j, k, l, m, p_1, q
Prism(poly1, h) → a, I, T, faceABJI, faceBCKJ, faceCDLK, faceADLI, face1, face2, face3, face4, face5, J, face6, faceIJKL, edgeAI, edgeBJ, edgeCK, edgeDL, edge1, edge3, edge5, edge7, K, edge9, edge11, edgeIJ, edgeJK, edgeKL, edgeIL, edge2, edge4, edge6, edge8, L, edge10, edge12, M, N, O, P, R
Net(a, net) → c, U, S_1, Z, A_1, B_1, C_1, D_1, E_1, K_1, L_1, M_1, V, N_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, W, J_2, F_1, I_1, J_1, T_1, U_1, V_1, W_1, Z_1, faceUVW, G_1, face8, face10, face9, face11, face12, face13, face14, face15, face16, face17, H_1, face7, edgeUV, edgeVW, edgeUW, edge25, edge26, edge38, edge39, edge40, edge41, O_1, edge42, edgeUZ, edge18, edge14, edge15, edge21, edge16, edge17, edge22, edge13, P_1, edge27, edge28, edge29, edge30, edge31, edge32, edge43, edge44, edge45, edge46, Q_1, edge47, edge48, edge49, edge50, edge51, edge52, edge53, edge54, edge55, edge56, R_1, edge57, edge20, edge19, edge23, edge24, edge33, edge34, edge35, edge36, edge37

AI Drawing Prompt Reference

Draw a regular polygon prism and its net. Start by placing a point as the center of a circle, draw a circle, pick a point on the circle, and connect the center to that point to form one edge. Use this edge to construct a regular polygon as the base. Then extrude this base upward by a given height to form a prism with rectangular side faces. Finally, unfold all faces of the prism onto a plane to create its net, which includes the base, top, and all side faces connected by edges, illustrating the transformation from 3D to 2D.

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