数値の整数比変換 と 双対多面体諸量
数値の整数比変換 と 双対多面体諸量 を求める Excel 画面を載せておきます。
どちらも すでにお伝えしている 計算式の 機能を追加したものです。
以後の 多面体製作の説明に 必要と思えたからです。
■角度や数値を整数比に換算する Excel 画面■ 色付けした全範囲を指定し 1 行目 A 列に copy and paste してください。 貼り付けのオプションは 貼り付け先の書式に合わせる(M)です。
| 298 | '=最大値+1 | =SMALL(D2:D81,1) | 桁数 | 4 | |||
| =A1-1 | =A2*($G$2) | =ROUND( B2,0) | =ROUND(ABS(B2-C2),$G$1) | =IF(D2=$E$1,B2," ") | 数値 | =H5 | |
| =A2-1 | =A3*($G$2) | =ROUND( B3,0) | =ROUND(ABS(B3-C3),$G$1) | =IF(D3=$E$1,B3," ") | |||
| =A3-1 | =A4*($G$2) | =ROUND( B4,0) | =ROUND(ABS(B4-C4),$G$1) | =IF(D4=$E$1,B4," ") | 寸法a | 0.5 | a/b |
| =A4-1 | =A5*($G$2) | =ROUND( B5,0) | =ROUND(ABS(B5-C5),$G$1) | =IF(D5=$E$1,B5," ") | 寸法b | =0.707106781186547 | =G4/G5 |
| =A5-1 | =A6*($G$2) | =ROUND( B6,0) | =ROUND(ABS(B6-C6),$G$1) | =IF(D6=$E$1,B6," ") | 対辺/底辺 | ||
| =A6-1 | =A7*($G$2) | =ROUND( B7,0) | =ROUND(ABS(B7-C7),$G$1) | =IF(D7=$E$1,B7," ") | 角度 | 54.7356103172453 | =TAN(RADIANS(G7)) |
■双対多面体の諸量を求める Excel 画面■ 色付けした全範囲を指定し 1 行目 A 列に copy and paste してください。 貼り付けのオプションは 貼り付け先の書式に合わせる(M)です。 ２４行目以降はデータです。各行のデータを２行目にcopy and paste してください。
| 名称 | S角数 | M角数 | L角数 | S面数 | M面数 | L面数 | 頂芯寸 | 双稜寸形 | ||
| 11 | [3,5,3,5] | 3 | 5 | 0 | 20 | 12 | 0 | 1.61803398874989 | SM 60 | |
| 角数 | 個数 | 多角形のかど心寸 | 面芯寸 | 多角形の辺心寸 | 面積 | 体積 | ||||
| =C2 | =F2 | =0.5/SIN(PI()/A5) | =SQRT($I$2^2-C5^2) | =0.5/TAN(PI()/A5) | =E5/2*A5*B5 | =F5*D5/3 | 総面積 | =SUM(F5:F7) | ||
| =D2 | =G2 | =IF(B6>0,0.5/SIN(PI()/A6),0) | =IF(B6>0,SQRT($I$2^2-C6^2),0) | =IF(B6>0,0.5/TAN(PI()/A6),0) | =IF(B6>0,E6/2*A6*B6,0) | =IF(B6>0,F6*D6/3,0) | ||||
| =E2 | =H2 | =IF(B7>0,0.5/SIN(PI()/A7),0) | =IF(B7>0,SQRT($I$2^2-C7^2),0) | =IF(B7>0,0.5/TAN(PI()/A7),0) | =IF(B7>0,E7/2*A7*B7,0) | =IF(B7>0,F7*D7/3,0) | 総体積 | =SUM(G5:G7) | SS 寸法 | |
| =G15*2 | ||||||||||
| かど角/2 (R) | かど心寸 | 辺心寸 | 稜芯寸 | 心・かど・芯角 | 双頂芯寸 | 双面芯寸 | SM 寸法 | |||
| =C2 | =F2 | =PI()/2-PI()/A10 | =0.5/COS(C10) | =0.5*TAN(C10) | =SQRT(I2^2-0.5^2) | =ACOS(D10/I2) | =F10^2/D5 | =H10*SIN(G10) | =G15+G16 | |
| =A6 | =G2 | =IF(B11>0,PI()/2-PI()/A11,0) | =IF(B11>0,0.5/COS(C11),0) | =IF(B11>0,0.5*TAN(C11),0) | =IF(B11>0,F10,"") | =IF(B11>0,ACOS(D11/I2),"") | =IF(B11>0,F11^2/D6,"") | =IF(B11>0,H11*SIN(G11),"") | SL 寸法 | |
| =A7 | =H2 | =IF(B12>0,PI()/2-PI()/A12,0) | =IF(B12>0,0.5/COS(C12),0) | =IF(B12>0,0.5*TAN(C12),0) | =IF(B12>0,F11,0) | =IF(B12>0,ACOS(D12/I2),0) | =IF(B12>0,F12^2/D7,0) | =IF(B12>0,H12*SIN(G12),0) | =G15+G17 | |
| MM 寸法 | ||||||||||
| 双菱形長寸 | 双菱形短寸/2 | 個別双面積 | 個別双体積 | 双稜寸 | 双稜開角/2 | 双対面積 | =G16+G16 | |||
| =A10 | =F2 | =H10*COS(G10) | =0.5*SIN(C10) | =C15*D15*A15*B15 | =E15*I10/3 | =SQRT(H10^2-F10^2) | =DEGREES(ASIN(D15/G15)) | =SUM(E15:E17) | ML 寸法 | |
| =A6 | =G2 | =IF(B16>0,H11*COS(G11),0) | =IF(B16>0,0.5*SIN(C11),0) | =IF(B16>0,C16*D16*A16*B16,0) | =IF(B16>0,E16*I11/3,0) | =IF(B16>0,SQRT(H11^2-F11^2),0) | =IF(B16>0,DEGREES(ASIN(D16/G16)),0) | 双対体積 | =G16+G17 | |
| =A7 | =H2 | =IF(B17>0,H12*COS(G12),0) | =IF(B17>0,0.5*SIN(C12),0) | =IF(B17>0,C17*D17*A17*B17,0) | =IF(B17>0,E17*I12/3,0) | =IF(B17>0,SQRT(H12^2-F12^2),0) | =IF(B17>0,DEGREES(ASIN(D17/G17)),0) | =SUM(F15:F17) | ||
| 面角 | 双対仰角 | 双接合角/2 | 双稜寸 / 稜芯寸 | =K2&" 必要" | ||||||
| =A10 | =F2 | =DEGREES(ACOS(E10/F10)) | =90-C20 | =90-DEGREES(C10) | =G15/F10 | |||||
| =A6 | =G2 | =IF(B21>0,DEGREES(ACOS(E11/F11)),0) | =IF(B21>0,90-C21,0) | =IF(B21>0,90-DEGREES(C11),0) | =IF(B16>0,G16/F11,0) | |||||
| =A7 | =H2 | =IF(B22>0,DEGREES(ACOS(E12/F12)),0) | =IF(B22>0,90-C22,0) | =IF(B22>0,90-DEGREES(C12),0) | =IF(B17>0,G17/F12,0) | |||||
| 名称 | S角数 | M角数 | L角数 | S面数 | M面数 | L面数 | 頂芯寸 | 双稜寸形 | ||
| 1 | [3,3,3] | 3 | 0 | 0 | 4 | 0 | 0 | 0.612372435695794 | SS 6 | |
| 2 | [3,3,3,3] | 3 | 0 | 0 | 8 | 0 | 0 | 0.707106781186547 | SS 12 | |
| 3 | [4,4,4] | 4 | 0 | 0 | 6 | 0 | 0 | 0.866025403784438 | SS 12 | |
| 4 | [3,3,3,3,3] | 3 | 0 | 0 | 20 | 0 | 0 | 0.951056516295153 | SS 30 | |
| 5 | [3,4,3,4] | 3 | 4 | 0 | 8 | 6 | 0 | 1 | SM 24 | |
| 6 | [3,6,6] | 3 | 6 | 0 | 4 | 4 | 0 | 1.17260393995585 | SM 12 MM 6 | |
| 7 | [3,3,3,3,4] | 3 | 4 | 0 | 32 | 6 | 0 | 1.3437133737446 | SS 36 SM 24 | |
| 8 | [3,4,4,4] | 3 | 4 | 0 | 8 | 18 | 0 | 1.3989663259659 | SM 24 MM 24 | |
| 9 | [5,5,5] | 5 | 0 | 0 | 12 | 0 | 0 | 1.40125853844407 | SS 30 | |
| 10 | [4,6,6] | 4 | 6 | 0 | 6 | 8 | 0 | 1.58113883008418 | SM 24 MM 12 | |
| 11 | [3,5,3,5] | 3 | 5 | 0 | 20 | 12 | 0 | 1.61803398874989 | SM 60 | |
| 12 | [3,8,8] | 3 | 8 | 0 | 8 | 6 | 0 | 1.77882364566392 | SM 24 MM 12 | |
| 13 | [3,3,3,3,5] | 3 | 5 | 0 | 80 | 12 | 0 | 2.15583737511563 | SS 90 SM 60 | |
| 14 | [3,4,5,4] | 3 | 4 | 5 | 20 | 30 | 12 | 2.23295050941569 | SM 60 ML 60 | |
| 15 | [4,6,8] | 4 | 6 | 8 | 12 | 8 | 6 | 2.31761091289276 | SM 24 SL 24 ML 24 | |
| 16 | [5,6,6] | 5 | 6 | 0 | 12 | 20 | 0 | 2.47801865906761 | SM 60 MM 30 | |
| 17 | [3,10,10] | 3 | 10 | 0 | 20 | 12 | 0 | 2.96944901586339 | SM 60 MM 30 | |
| 18 | [4,6,10] | 4 | 6 | 10 | 30 | 20 | 12 | 3.80239449985129 | SM 60 SL 60 ML 60 | |
2016年8月3日
