Developmental Geometry for a Pyramid with an (6 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 60
working angle = 30
plan angle = 60
miter angle = 6.93 & 12
hip run per foot = 13.856406460551
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.15470053837925
side_wall_multiplier = 1.15470053837925
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 41.56922 41.56922 48.00000 48.00000 0.00000 0.00000 30.00000 0.00000 30.00000 60.00000 41.56922 48.00000 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 0.00000 30.00000 60.00000
1.00 48.00000 41.56922 41.56922 48.00000 48.00000 4.76364 4.12781 29.93560 2.37976 29.91423 60.08577 41.71331 48.12484 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 2.74502 29.88580 59.84436
2.00 48.00000 41.56922 41.56922 48.00000 48.00000 9.46232 8.21321 29.74488 4.71500 29.66129 60.33871 42.14262 48.49742 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 5.42203 29.55093 59.38460
3.00 48.00000 41.56922 41.56922 48.00000 48.00000 14.03624 12.21635 29.43502 6.96528 29.25371 60.74629 42.84857 49.11212 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 7.97118 29.01714 58.64133
4.00 48.00000 41.56922 41.56922 48.00000 48.00000 18.43495 16.10211 29.01714 9.09744 28.71051 61.28949 43.81780 49.95998 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 10.34677 28.31649 57.64614
5.00 48.00000 41.56922 41.56922 48.00000 48.00000 22.61986 19.84167 28.50530 11.08749 28.05488 61.94512 45.03332 51.02940 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 12.51983 27.48643 56.43805
6.00 48.00000 41.56922 41.56922 48.00000 48.00000 26.56505 23.41322 27.91522 12.92097 27.31173 62.68827 46.47580 52.30679 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 14.47751 26.56505 55.05978
7.00 48.00000 41.56922 41.56922 48.00000 48.00000 30.25644 26.80206 27.26320 14.59208 26.50557 63.49443 48.12484 53.77732 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 16.22025 25.58753 53.55418
8.00 48.00000 41.56922 41.56922 48.00000 48.00000 33.69007 30.00000 26.56505 16.10211 25.65891 64.34109 49.95998 55.42563 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 17.75799 24.58389 51.96152
9.00 48.00000 41.56922 41.56922 48.00000 48.00000 36.86990 33.00449 25.83543 17.45760 24.79128 65.20872 51.96152 57.23635 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 19.10661 23.57818 50.31767
10.00 48.00000 41.56922 41.56922 48.00000 48.00000 39.80557 35.81753 25.08733 18.66850 23.91885 66.08115 54.11100 59.19459 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 20.28485 22.58854 48.65309
11.00 48.00000 41.56922 41.56922 48.00000 48.00000 42.51045 38.44454 24.33185 19.74669 23.05442 66.94558 56.39149 61.28621 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 21.31224 21.62789 46.99262
12.00 48.00000 41.56922 41.56922 48.00000 48.00000 45.00000 40.89339 23.57818 20.70481 22.20765 67.79235 58.78775 63.49803 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 22.20765 20.70481 45.35574
13.00 48.00000 41.56922 41.56922 48.00000 48.00000 47.29061 43.17355 22.83365 21.55546 21.38557 68.61443 61.28621 65.81793 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 22.98855 19.82449 43.75707
14.00 48.00000 41.56922 41.56922 48.00000 48.00000 49.39871 45.29534 22.10396 22.31066 20.59294 69.40706 63.87488 68.23489 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 23.67058 18.98955 42.20715
15.00 48.00000 41.56922 41.56922 48.00000 48.00000 51.34019 47.26947 21.39334 22.98153 19.83274 70.16726 66.54322 70.73896 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 24.26751 18.20076 40.71307
16.00 48.00000 41.56922 41.56922 48.00000 48.00000 53.13010 49.10661 20.70481 23.57818 19.10661 70.89339 69.28203 73.32121 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 24.79128 17.45760 39.27922
17.00 48.00000 41.56922 41.56922 48.00000 48.00000 54.78241 50.81712 20.04038 24.10963 18.41509 71.58491 72.08329 75.97368 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 25.25216 16.75870 37.90787
18.00 48.00000 41.56922 41.56922 48.00000 48.00000 56.30993 52.41091 19.40126 24.58389 17.75799 72.24201 74.93998 78.68926 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 25.65891 16.10211 36.59966
19.00 48.00000 41.56922 41.56922 48.00000 48.00000 57.72436 53.89731 18.78803 25.00798 17.13458 72.86542 77.84600 81.46165 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 26.01900 15.48562 35.35406
20.00 48.00000 41.56922 41.56922 48.00000 48.00000 59.03624 55.28500 18.20076 25.38803 16.54375 73.45625 80.79604 84.28523 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 26.33880 14.90682 34.16969
21.00 48.00000 41.56922 41.56922 48.00000 48.00000 60.25512 56.58202 17.63918 25.72941 15.98415 74.01585 83.78544 87.15503 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 26.62371 14.36330 33.04456
22.00 48.00000 41.56922 41.56922 48.00000 48.00000 61.38954 57.79577 17.10273 26.03677 15.45428 74.54572 86.81014 90.06664 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 26.87832 13.85267 31.97632
23.00 48.00000 41.56922 41.56922 48.00000 48.00000 62.44719 58.93304 16.59067 26.31414 14.95259 75.04741 89.86657 93.01613 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 27.10654 13.37262 30.96237
24.00 48.00000 41.56922 41.56922 48.00000 48.00000 63.43495 60.00000 16.10211 26.56505 14.47751 75.52249 92.95160 96.00000 83.13844 48.00000 60.00000 24.00000 30.00000 41.56922 301.59289 27.31173 12.92097 30.00000
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 = 60.00000
Roof Surface Angle C Bay # 0 = 60.00000
Roof Surface Angle B Bay # 0 = 60.00000

Roof Surface Angle A Bay # 1 = 60.08577
Roof Surface Angle C Bay # 1 = 59.82845
Roof Surface Angle B Bay # 1 = 60.08577

Roof Surface Angle A Bay # 2 = 60.33871
Roof Surface Angle C Bay # 2 = 59.32258
Roof Surface Angle B Bay # 2 = 60.33871

Roof Surface Angle A Bay # 3 = 60.74629
Roof Surface Angle C Bay # 3 = 58.50743
Roof Surface Angle B Bay # 3 = 60.74629

Roof Surface Angle A Bay # 4 = 61.28949
Roof Surface Angle C Bay # 4 = 57.42103
Roof Surface Angle B Bay # 4 = 61.28949

Roof Surface Angle A Bay # 5 = 61.94512
Roof Surface Angle C Bay # 5 = 56.10976
Roof Surface Angle B Bay # 5 = 61.94512

Roof Surface Angle A Bay # 6 = 62.68827
Roof Surface Angle C Bay # 6 = 54.62346
Roof Surface Angle B Bay # 6 = 62.68827

Roof Surface Angle A Bay # 7 = 63.49443
Roof Surface Angle C Bay # 7 = 53.01114
Roof Surface Angle B Bay # 7 = 63.49443

Roof Surface Angle A Bay # 8 = 64.34109
Roof Surface Angle C Bay # 8 = 51.31781
Roof Surface Angle B Bay # 8 = 64.34109

Roof Surface Angle A Bay # 9 = 65.20872
Roof Surface Angle C Bay # 9 = 49.58256
Roof Surface Angle B Bay # 9 = 65.20872

Roof Surface Angle A Bay # 10 = 66.08115
Roof Surface Angle C Bay # 10 = 47.83771
Roof Surface Angle B Bay # 10 = 66.08115

Roof Surface Angle A Bay # 11 = 66.94558
Roof Surface Angle C Bay # 11 = 46.10883
Roof Surface Angle B Bay # 11 = 66.94558

Roof Surface Angle A Bay # 12 = 67.79235
Roof Surface Angle C Bay # 12 = 44.41531
Roof Surface Angle B Bay # 12 = 67.79235

Roof Surface Angle A Bay # 13 = 68.61443
Roof Surface Angle C Bay # 13 = 42.77114
Roof Surface Angle B Bay # 13 = 68.61443

Roof Surface Angle A Bay # 14 = 69.40706
Roof Surface Angle C Bay # 14 = 41.18587
Roof Surface Angle B Bay # 14 = 69.40706

Roof Surface Angle A Bay # 15 = 70.16726
Roof Surface Angle C Bay # 15 = 39.66549
Roof Surface Angle B Bay # 15 = 70.16726

Roof Surface Angle A Bay # 16 = 70.89339
Roof Surface Angle C Bay # 16 = 38.21321
Roof Surface Angle B Bay # 16 = 70.89339

Roof Surface Angle A Bay # 17 = 71.58491
Roof Surface Angle C Bay # 17 = 36.83017
Roof Surface Angle B Bay # 17 = 71.58491

Roof Surface Angle A Bay # 18 = 72.24201
Roof Surface Angle C Bay # 18 = 35.51598
Roof Surface Angle B Bay # 18 = 72.24201

Roof Surface Angle A Bay # 19 = 72.86542
Roof Surface Angle C Bay # 19 = 34.26917
Roof Surface Angle B Bay # 19 = 72.86542

Roof Surface Angle A Bay # 20 = 73.45625
Roof Surface Angle C Bay # 20 = 33.08750
Roof Surface Angle B Bay # 20 = 73.45625

Roof Surface Angle A Bay # 21 = 74.01585
Roof Surface Angle C Bay # 21 = 31.96829
Roof Surface Angle B Bay # 21 = 74.01585

Roof Surface Angle A Bay # 22 = 74.54572
Roof Surface Angle C Bay # 22 = 30.90856
Roof Surface Angle B Bay # 22 = 74.54572

Roof Surface Angle A Bay # 23 = 75.04741
Roof Surface Angle C Bay # 23 = 29.90519
Roof Surface Angle B Bay # 23 = 75.04741

Roof Surface Angle A Bay # 24 = 75.52249
Roof Surface Angle C Bay # 24 = 28.95502
Roof Surface Angle B Bay # 24 = 75.52249

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