Developmental Geometry for a Pyramid with an (36 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 10
working angle = 5
plan angle = 85
miter angle = 1.05 & 12
hip run per foot = 12.0458380505202
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.00381983754335
side_wall_multiplier = 0.174977327051848
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 47.81735 47.81735 48.00000 8.36695 0.00000 0.00000 5.00000 0.00000 5.00000 85.00000 47.81735 48.00000 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 0.00000 5.00000 10.00000
1.00 48.00000 47.81735 47.81735 48.00000 8.36695 4.76364 4.74560 4.98295 0.41470 4.98282 85.01718 47.98309 48.16512 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 0.41628 4.98269 9.96572
2.00 48.00000 47.81735 47.81735 48.00000 8.36695 9.46232 9.42696 4.93281 0.82098 4.93231 85.06769 48.47693 48.65710 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 0.82403 4.93180 9.86495
3.00 48.00000 47.81735 47.81735 48.00000 8.36695 14.03624 13.98493 4.85251 1.21123 4.85144 85.14856 49.28899 49.46621 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 1.21558 4.85035 9.70359
4.00 48.00000 47.81735 47.81735 48.00000 8.36695 18.43495 18.36952 4.74641 1.57933 4.74462 85.25538 50.40391 50.57722 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 1.58476 4.74281 9.49044
5.00 48.00000 47.81735 47.81735 48.00000 8.36695 22.61986 22.54242 4.61970 1.92100 4.61712 85.38288 51.80212 51.97078 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 1.92725 4.61452 9.23596
6.00 48.00000 47.81735 47.81735 48.00000 8.36695 26.56505 26.47777 4.47779 2.23380 4.47441 85.52559 53.46142 53.62485 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 2.24062 4.47100 8.95107
7.00 48.00000 47.81735 47.81735 48.00000 8.36695 30.25644 30.16145 4.32583 2.51697 4.32168 85.67832 55.35832 55.51617 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 2.52414 4.31750 8.64613
8.00 48.00000 47.81735 47.81735 48.00000 8.36695 33.69007 33.58932 4.16836 2.77106 4.16350 85.83650 57.46930 57.62136 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 2.77838 4.15862 8.33024
9.00 48.00000 47.81735 47.81735 48.00000 8.36695 36.86990 36.76510 4.00912 2.99756 4.00366 85.99634 59.77168 59.91791 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 3.00488 3.99817 8.01096
10.00 48.00000 47.81735 47.81735 48.00000 8.36695 39.80557 39.69818 3.85109 3.19852 3.84510 86.15490 62.24423 62.38466 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 3.20572 3.83911 7.69420
11.00 48.00000 47.81735 47.81735 48.00000 8.36695 42.51045 42.40166 3.69644 3.37629 3.69005 86.30995 64.86750 65.00226 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 3.38329 3.68363 7.38436
12.00 48.00000 47.81735 47.81735 48.00000 8.36695 45.00000 44.89078 3.54675 3.53329 3.54002 86.45998 67.62394 67.75322 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 3.54002 3.53329 7.08453
13.00 48.00000 47.81735 47.81735 48.00000 8.36695 47.29061 47.18172 3.40302 3.67187 3.39605 86.60395 70.49793 70.62195 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 3.67831 3.38907 6.79675
14.00 48.00000 47.81735 47.81735 48.00000 8.36695 49.39871 49.29074 3.26587 3.79424 3.25872 86.74128 73.47569 73.59469 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 3.80037 3.25157 6.52221
15.00 48.00000 47.81735 47.81735 48.00000 8.36695 51.34019 51.23359 3.13557 3.90241 3.12832 86.87168 76.54510 76.65934 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 3.90821 3.12106 6.26147
16.00 48.00000 47.81735 47.81735 48.00000 8.36695 53.13010 53.02519 3.01220 3.99817 3.00488 86.99512 79.69558 79.80530 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.00366 2.99756 6.01464
17.00 48.00000 47.81735 47.81735 48.00000 8.36695 54.78241 54.67943 2.89565 4.08311 2.88831 87.11169 82.91788 83.02334 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.08829 2.88097 5.78151
18.00 48.00000 47.81735 47.81735 48.00000 8.36695 56.30993 56.20904 2.78571 4.15862 2.77838 87.22162 86.20395 86.30540 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.16350 2.77106 5.56165
19.00 48.00000 47.81735 47.81735 48.00000 8.36695 57.72436 57.62565 2.68210 4.22591 2.67482 87.32518 89.54677 89.64444 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.23050 2.66754 5.35449
20.00 48.00000 47.81735 47.81735 48.00000 8.36695 59.03624 58.93978 2.58451 4.28602 2.57729 87.42271 92.94021 93.03432 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.29034 2.57008 5.15939
21.00 48.00000 47.81735 47.81735 48.00000 8.36695 60.25512 60.16093 2.49259 4.33986 2.48545 87.51455 96.37894 96.46969 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.34393 2.47832 4.97566
22.00 48.00000 47.81735 47.81735 48.00000 8.36695 61.38954 61.29762 2.40600 4.38820 2.39895 87.60105 99.85827 99.94586 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.39203 2.39192 4.80260
23.00 48.00000 47.81735 47.81735 48.00000 8.36695 62.44719 62.35751 2.32440 4.43172 2.31745 87.68255 103.37410 103.45872 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.43533 2.31052 4.63953
24.00 48.00000 47.81735 47.81735 48.00000 8.36695 63.43495 63.34747 2.24745 4.47100 2.24062 87.75938 106.92284 107.00465 95.63469 8.36695 10.00000 8.23984 80.00000 1.45291 301.59289 4.47441 2.23380 4.48579
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 = 85.00000
Roof Surface Angle C Bay # 0 = 10.00000
Roof Surface Angle B Bay # 0 = 85.00000

Roof Surface Angle A Bay # 1 = 85.01718
Roof Surface Angle C Bay # 1 = 9.96563
Roof Surface Angle B Bay # 1 = 85.01718

Roof Surface Angle A Bay # 2 = 85.06769
Roof Surface Angle C Bay # 2 = 9.86462
Roof Surface Angle B Bay # 2 = 85.06769

Roof Surface Angle A Bay # 3 = 85.14856
Roof Surface Angle C Bay # 3 = 9.70287
Roof Surface Angle B Bay # 3 = 85.14856

Roof Surface Angle A Bay # 4 = 85.25538
Roof Surface Angle C Bay # 4 = 9.48924
Roof Surface Angle B Bay # 4 = 85.25538

Roof Surface Angle A Bay # 5 = 85.38288
Roof Surface Angle C Bay # 5 = 9.23423
Roof Surface Angle B Bay # 5 = 85.38288

Roof Surface Angle A Bay # 6 = 85.52559
Roof Surface Angle C Bay # 6 = 8.94881
Roof Surface Angle B Bay # 6 = 85.52559

Roof Surface Angle A Bay # 7 = 85.67832
Roof Surface Angle C Bay # 7 = 8.64335
Roof Surface Angle B Bay # 7 = 85.67832

Roof Surface Angle A Bay # 8 = 85.83650
Roof Surface Angle C Bay # 8 = 8.32700
Roof Surface Angle B Bay # 8 = 85.83650

Roof Surface Angle A Bay # 9 = 85.99634
Roof Surface Angle C Bay # 9 = 8.00731
Roof Surface Angle B Bay # 9 = 85.99634

Roof Surface Angle A Bay # 10 = 86.15490
Roof Surface Angle C Bay # 10 = 7.69021
Roof Surface Angle B Bay # 10 = 86.15490

Roof Surface Angle A Bay # 11 = 86.30995
Roof Surface Angle C Bay # 11 = 7.38009
Roof Surface Angle B Bay # 11 = 86.30995

Roof Surface Angle A Bay # 12 = 86.45998
Roof Surface Angle C Bay # 12 = 7.08005
Roof Surface Angle B Bay # 12 = 86.45998

Roof Surface Angle A Bay # 13 = 86.60395
Roof Surface Angle C Bay # 13 = 6.79211
Roof Surface Angle B Bay # 13 = 86.60395

Roof Surface Angle A Bay # 14 = 86.74128
Roof Surface Angle C Bay # 14 = 6.51745
Roof Surface Angle B Bay # 14 = 86.74128

Roof Surface Angle A Bay # 15 = 86.87168
Roof Surface Angle C Bay # 15 = 6.25663
Roof Surface Angle B Bay # 15 = 86.87168

Roof Surface Angle A Bay # 16 = 86.99512
Roof Surface Angle C Bay # 16 = 6.00976
Roof Surface Angle B Bay # 16 = 86.99512

Roof Surface Angle A Bay # 17 = 87.11169
Roof Surface Angle C Bay # 17 = 5.77662
Roof Surface Angle B Bay # 17 = 87.11169

Roof Surface Angle A Bay # 18 = 87.22162
Roof Surface Angle C Bay # 18 = 5.55677
Roof Surface Angle B Bay # 18 = 87.22162

Roof Surface Angle A Bay # 19 = 87.32518
Roof Surface Angle C Bay # 19 = 5.34964
Roof Surface Angle B Bay # 19 = 87.32518

Roof Surface Angle A Bay # 20 = 87.42271
Roof Surface Angle C Bay # 20 = 5.15458
Roof Surface Angle B Bay # 20 = 87.42271

Roof Surface Angle A Bay # 21 = 87.51455
Roof Surface Angle C Bay # 21 = 4.97090
Roof Surface Angle B Bay # 21 = 87.51455

Roof Surface Angle A Bay # 22 = 87.60105
Roof Surface Angle C Bay # 22 = 4.79791
Roof Surface Angle B Bay # 22 = 87.60105

Roof Surface Angle A Bay # 23 = 87.68255
Roof Surface Angle C Bay # 23 = 4.63491
Roof Surface Angle B Bay # 23 = 87.68255

Roof Surface Angle A Bay # 24 = 87.75938
Roof Surface Angle C Bay # 24 = 4.48124
Roof Surface Angle B Bay # 24 = 87.75938