Developmental Geometry for a Pyramid with an (96 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places
Pitch | Radius | apothem | radius ÷ apothem multiplier | apothem multiplier * apothem | side wall multiplier * apothem | Pitch Angle | Hip Angle | Hip Side Cut Angle | Hip Backing Angle | Jack Rafter Side Cut Angle | Jack Rafter Side Cut Angle 2 | Rafter Length | Hip Length | Span | Wall Length | Projection Angle A | Projection A | Projection Angle B | Projection B | Circumference | Freize Block Miter Angle | Freize Block Bevel Angle | Surface Angle |
0.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 0.00000 | 0.00000 | 1.87500 | 0.00000 | 1.87500 | 88.12500 | 47.97430 | 48.00000 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.00000 | 1.87500 | 3.75000 |
1.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 4.76364 | 4.76110 | 1.86853 | 0.15568 | 1.86853 | 88.13147 | 48.14059 | 48.16620 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.15577 | 1.86852 | 3.73706 |
2.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 9.46232 | 9.45735 | 1.84953 | 0.30819 | 1.84951 | 88.15049 | 48.63605 | 48.66140 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.30836 | 1.84948 | 3.69903 |
3.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 14.03624 | 14.02903 | 1.81911 | 0.45468 | 1.81906 | 88.18094 | 49.45078 | 49.47571 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.45491 | 1.81900 | 3.63815 |
4.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 18.43495 | 18.42575 | 1.77894 | 0.59283 | 1.77884 | 88.22116 | 50.56935 | 50.59373 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.59312 | 1.77875 | 3.55775 |
5.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 22.61986 | 22.60897 | 1.73100 | 0.72104 | 1.73086 | 88.26914 | 51.97216 | 51.99588 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.72137 | 1.73072 | 3.46181 |
6.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 26.56505 | 26.55278 | 1.67735 | 0.83841 | 1.67717 | 88.32283 | 53.63690 | 53.65989 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.83877 | 1.67699 | 3.35446 |
7.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 30.25644 | 30.24308 | 1.61995 | 0.94463 | 1.61973 | 88.38027 | 55.54002 | 55.56222 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 0.94501 | 1.61951 | 3.23961 |
8.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 33.69007 | 33.67591 | 1.56052 | 1.03993 | 1.56027 | 88.43973 | 57.65793 | 57.67932 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.04032 | 1.56001 | 3.12070 |
9.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 36.86990 | 36.85517 | 1.50048 | 1.12487 | 1.50019 | 88.49981 | 59.96788 | 59.98844 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.12526 | 1.49990 | 3.00058 |
10.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 39.80557 | 39.79048 | 1.44094 | 1.20022 | 1.44063 | 88.55937 | 62.44854 | 62.46829 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.20060 | 1.44031 | 2.88146 |
11.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 42.51045 | 42.49516 | 1.38273 | 1.26686 | 1.38239 | 88.61761 | 65.08042 | 65.09937 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.26723 | 1.38205 | 2.76500 |
12.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 45.00000 | 44.98466 | 1.32642 | 1.32571 | 1.32606 | 88.67394 | 67.84591 | 67.86408 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.32606 | 1.32571 | 2.65236 |
13.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 47.29061 | 47.27532 | 1.27239 | 1.37764 | 1.27202 | 88.72798 | 70.72933 | 70.74677 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.37798 | 1.27165 | 2.54429 |
14.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 49.39871 | 49.38354 | 1.22086 | 1.42350 | 1.22048 | 88.77952 | 73.71687 | 73.73359 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.42382 | 1.22011 | 2.44122 |
15.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 51.34019 | 51.32522 | 1.17194 | 1.46403 | 1.17156 | 88.82844 | 76.79635 | 76.81241 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.46433 | 1.17118 | 2.34337 |
16.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 53.13010 | 53.11537 | 1.12564 | 1.49990 | 1.12526 | 88.87474 | 79.95717 | 79.97259 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.50019 | 1.12487 | 2.25077 |
17.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 54.78241 | 54.76795 | 1.08193 | 1.53172 | 1.08154 | 88.91846 | 83.19004 | 83.20487 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.53200 | 1.08115 | 2.16333 |
18.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 56.30993 | 56.29577 | 1.04071 | 1.56001 | 1.04032 | 88.95968 | 86.48690 | 86.50116 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.56027 | 1.03993 | 2.08090 |
19.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 57.72436 | 57.71050 | 1.00188 | 1.58521 | 1.00149 | 88.99851 | 89.84069 | 89.85442 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.58545 | 1.00111 | 2.00324 |
20.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 59.03624 | 59.02270 | 0.96531 | 1.60772 | 0.96493 | 89.03507 | 93.24528 | 93.25850 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.60795 | 0.96455 | 1.93012 |
21.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 60.25512 | 60.24190 | 0.93089 | 1.62788 | 0.93051 | 89.06949 | 96.69529 | 96.70805 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.62810 | 0.93014 | 1.86127 |
22.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 61.38954 | 61.37664 | 0.89847 | 1.64599 | 0.89809 | 89.10191 | 100.18604 | 100.19835 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.64619 | 0.89772 | 1.79644 |
23.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 62.44719 | 62.43460 | 0.86792 | 1.66228 | 0.86755 | 89.13245 | 103.71341 | 103.72531 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.66247 | 0.86719 | 1.73535 |
24.00 | 48.00000 | 47.97430 | 47.97430 | 48.00000 | 3.14103 | 63.43495 | 63.42267 | 0.83912 | 1.67699 | 0.83877 | 89.16123 | 107.27380 | 107.28529 | 95.94860 | 3.14103 | 3.75000 | 3.13431 | 86.25000 | 0.20543 | 301.59289 | 1.67717 | 0.83841 | 1.67777 |
Pitch | Radius | apothem | radius ÷ apothem multiplier | apothem multiplier * apothem | side wall multiplier * apothem | Pitch Angle | Hip Angle | Hip Side Cut Angle | Hip Backing Angle | Jack Rafter Side Cut Angle | Jack Rafter Side Cut Angle 2 | Rafter Length | Hip Length | Span | Wall Length | Projection Angle A | Projection A | Projection Angle B | Projection B | Circumference | Freize Block Miter Angle | Freize Block Bevel Angle | Surface Angle |
Roof Surface Angle A Bay # 0 = 88.12500°
Roof Surface Angle C Bay # 0 = 3.75000°
Roof Surface Angle B Bay # 0 = 88.12500°
Roof Surface Angle A Bay # 1 = 88.13147°
Roof Surface Angle C Bay # 1 = 3.73706°
Roof Surface Angle B Bay # 1 = 88.13147°
Roof Surface Angle A Bay # 2 = 88.15049°
Roof Surface Angle C Bay # 2 = 3.69901°
Roof Surface Angle B Bay # 2 = 88.15049°
Roof Surface Angle A Bay # 3 = 88.18094°
Roof Surface Angle C Bay # 3 = 3.63811°
Roof Surface Angle B Bay # 3 = 88.18094°
Roof Surface Angle A Bay # 4 = 88.22116°
Roof Surface Angle C Bay # 4 = 3.55769°
Roof Surface Angle B Bay # 4 = 88.22116°
Roof Surface Angle A Bay # 5 = 88.26914°
Roof Surface Angle C Bay # 5 = 3.46172°
Roof Surface Angle B Bay # 5 = 88.26914°
Roof Surface Angle A Bay # 6 = 88.32283°
Roof Surface Angle C Bay # 6 = 3.35434°
Roof Surface Angle B Bay # 6 = 88.32283°
Roof Surface Angle A Bay # 7 = 88.38027°
Roof Surface Angle C Bay # 7 = 3.23946°
Roof Surface Angle B Bay # 7 = 88.38027°
Roof Surface Angle A Bay # 8 = 88.43973°
Roof Surface Angle C Bay # 8 = 3.12053°
Roof Surface Angle B Bay # 8 = 88.43973°
Roof Surface Angle A Bay # 9 = 88.49981°
Roof Surface Angle C Bay # 9 = 3.00039°
Roof Surface Angle B Bay # 9 = 88.49981°
Roof Surface Angle A Bay # 10 = 88.55937°
Roof Surface Angle C Bay # 10 = 2.88125°
Roof Surface Angle B Bay # 10 = 88.55937°
Roof Surface Angle A Bay # 11 = 88.61761°
Roof Surface Angle C Bay # 11 = 2.76478°
Roof Surface Angle B Bay # 11 = 88.61761°
Roof Surface Angle A Bay # 12 = 88.67394°
Roof Surface Angle C Bay # 12 = 2.65212°
Roof Surface Angle B Bay # 12 = 88.67394°
Roof Surface Angle A Bay # 13 = 88.72798°
Roof Surface Angle C Bay # 13 = 2.54404°
Roof Surface Angle B Bay # 13 = 88.72798°
Roof Surface Angle A Bay # 14 = 88.77952°
Roof Surface Angle C Bay # 14 = 2.44097°
Roof Surface Angle B Bay # 14 = 88.77952°
Roof Surface Angle A Bay # 15 = 88.82844°
Roof Surface Angle C Bay # 15 = 2.34312°
Roof Surface Angle B Bay # 15 = 88.82844°
Roof Surface Angle A Bay # 16 = 88.87474°
Roof Surface Angle C Bay # 16 = 2.25051°
Roof Surface Angle B Bay # 16 = 88.87474°
Roof Surface Angle A Bay # 17 = 88.91846°
Roof Surface Angle C Bay # 17 = 2.16308°
Roof Surface Angle B Bay # 17 = 88.91846°
Roof Surface Angle A Bay # 18 = 88.95968°
Roof Surface Angle C Bay # 18 = 2.08064°
Roof Surface Angle B Bay # 18 = 88.95968°
Roof Surface Angle A Bay # 19 = 88.99851°
Roof Surface Angle C Bay # 19 = 2.00298°
Roof Surface Angle B Bay # 19 = 88.99851°
Roof Surface Angle A Bay # 20 = 89.03507°
Roof Surface Angle C Bay # 20 = 1.92987°
Roof Surface Angle B Bay # 20 = 89.03507°
Roof Surface Angle A Bay # 21 = 89.06949°
Roof Surface Angle C Bay # 21 = 1.86102°
Roof Surface Angle B Bay # 21 = 89.06949°
Roof Surface Angle A Bay # 22 = 89.10191°
Roof Surface Angle C Bay # 22 = 1.79619°
Roof Surface Angle B Bay # 22 = 89.10191°
Roof Surface Angle A Bay # 23 = 89.13245°
Roof Surface Angle C Bay # 23 = 1.73511°
Roof Surface Angle B Bay # 23 = 89.13245°
Roof Surface Angle A Bay # 24 = 89.16123°
Roof Surface Angle C Bay # 24 = 1.67753°
Roof Surface Angle B Bay # 24 = 89.16123°