算額是日本的幾何問題木板的定理，在江戶時代被作為祭祀或祭品神道的神社里。算額數學雜誌的第一期於2017年出版。算額數學雜誌是一份開放性的電子期刊，力作於研究傳統和讃中的幾何問題。在這篇論文中，我們將聚焦在矩形算額的作圖上，這些圖形是由平面上的7個圓圈所構成，每個圓至少與其他三個圓有相切關係。如果將這平面上的7個圓圈反演至同一個球面上，將保留其相切關係。這篇論文共做出了16個這樣的矩形算額，每個矩形算額都可以使用固定的方法來構造一個外切七面體，並且與其他15個外切七面體具有不同拓樸構造。

Sangaku are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines during the Edo period. The first volume of the Sangaku Journal of Mathematics was pub-lished in 2017. Sangaku Journal of Mathematics is an open-access elec-tronic journal devoted to geometry problems in the Wasan tradition. In this work, we shall restrict to the construction of rectangular sangaku fig-ures each of circles is tangent to at least three others, the collection of 7-circle figures in a plane which can be inverted to 7 circles on a sphere that retains the relation of tangence. This paper establishes 16 such rec-tangular sangaku figures each of which can be then used as an algorithm to construct a circumscriptible heptahedron topologically distinct from 15 others.

Abstract ...................................2
0. Preliminary..............................4
0.1 Research settings.......................4
0.2 Circumscriptible polyhedron.............4
0.3 Inversion...............................4
0.4 Stereographic Projection................5
0.5 List of 34 topologically distinct convex heptahedrons in Wikipedia ............................................7
1. Motivation for constructing a circumscriptible heptahedron by means of a sangaku figure.........................9
1.1 An illustration of (6,6,4,4,4,3,3)......9
1.2 Properties..............................10
1.3 Non-Uniqueness..........................11
1.4 Any two disjoint circles on a sphere can be inverted into two circles having the same axis................12
1.5 Construct circumscriptible heptahedrons by 7-circle sangaku figures.....................................14
2. Circumscriptible heptahedrons constructed by truncating circumscriptible hexahedrons................15
2.1 Summary of the main result..............15
2.2 All possibilities of forming a 7-circle sangaku figure from a 6-circle sangaku figure.......................16
3. Concrete examples of equivalent sangaku figures ............................................22
4. Reference................................25

[1] Cabri 3D, a dynamic mathematical software in space. Cabrilog, 2004,
Cabri 3D - Discovering the 3rd dimension | Cabrilog
[2] Altshiller-Court, Nathan, Modern Pure Solid Geometry, Macmillan, New York, 1935
[3] Coxeter H. S. M., Introduction to Geometry 2nd edition, New York, 1969
[4] Topologically distinct heptahedron, Heptahedron, Wikipedia. Available at https://en.wikipedia.org/wiki/Heptahedron
[5] This work is completed under the environment provided by Google Workspace. Available at
https://drive.google.com/drive/folders/10_Z8HMBYsIVyWJ9vAu9SbUu_VfAT8mI9