我們知道七面體有34種拓樸不同構的型態，藉由Cabri 3D，選擇其中幾個討論並利用反演去建構甚至做出其對偶。
首先我們利用球心到球面上的點的距離都相同的性質去將做出來的七面體使其邊相切於球。再來利用七面體與球的切點以及對偶的邊會和原圖形的邊互相垂直之性質去做出其對偶。
最後我們試著去用較少的步驟去製造七面體，甚至是利用"Sangaku"的技巧將平面上的圖形投影到球面上以求得七面體。

We know that there are 34 topologically distinct convex heptahedra and choose some heptahedra using inversion to construct them as well as their duals by Cabri 3D.
First, I make use of the technique that the same distance between center point and any points which lie on the spherical surface to construct the heptahedra which edges are tangential with the sphere.
Second, I use the cut-off points to connect the lines which plumb the edges of heptahedra and pass through the cut-off points. From the intersection points of this lines, we can depict the dualities.
At last, I attempt to search some skills to build the heptahedra with less steps. In addition, the technology inversion with "Sangaku" make the constructions of heptahedra easier. In my thesis, I use Cabri 3D to construct the heptahedra.

[1] https://en.wikipedia.org/wiki/Heptahedron
[2] https://mathoverflow.net/questions/25829/maximum-number-of-shortest-paths
[3] A Geometrical Picture Book, Burkard Polster p.4
[4] https://en.wikipedia.org/wiki/Inversive_geometry
[5 ] Sacred Mathematics, Tony Rothman