Developmental Geometry for a Pyramid with an (96 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 3.75
working angle = 1.875
plan angle = 88.125
miter angle = 0.39 & 12
hip run per foot = 12.0064283921253
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.00053569934377
side_wall_multiplier = 0.0654732208259452
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