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


central angle = 72
working angle = 36
plan angle = 54
miter angle = 8.72 & 12
hip run per foot = 14.8328157299975
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.23606797749979
side_wall_multiplier = 1.45308505601072
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 38.83282 38.83282 48.00000 56.42738 0.00000 0.00000 36.00000 0.00000 36.00000 54.00000 38.83282 48.00000 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 0.00000 36.00000 72.00000
1.00 48.00000 38.83282 38.83282 48.00000 56.42738 4.76364 3.85694 35.93824 2.79789 35.90577 54.09423 38.96742 48.10896 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 3.45282 35.85634 71.83693
2.00 48.00000 38.83282 38.83282 48.00000 56.42738 9.46232 7.67923 35.75489 5.54522 35.62755 54.37245 39.36847 48.43437 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 6.81130 35.43562 71.35428
3.00 48.00000 38.83282 38.83282 48.00000 56.42738 14.03624 11.43407 35.45555 8.19594 35.17809 54.82191 40.02795 48.97192 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 9.99364 34.76665 70.57105
4.00 48.00000 38.83282 38.83282 48.00000 56.42738 18.43495 15.09208 35.04901 10.71209 34.57689 55.42311 40.93338 49.71473 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 12.93932 33.89151 69.51662
5.00 48.00000 38.83282 38.83282 48.00000 56.42738 22.61986 18.62847 34.54659 13.06588 33.84796 56.15204 42.06888 50.65376 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 15.61246 32.85883 68.22791
6.00 48.00000 38.83282 38.83282 48.00000 56.42738 26.56505 22.02375 33.96128 15.24016 33.01740 56.98260 43.41641 51.77834 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 18.00000 31.71747 66.74605
7.00 48.00000 38.83282 38.83282 48.00000 56.42738 30.25644 25.26387 33.30692 17.22759 32.11124 57.88876 44.95689 53.07669 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 20.10686 30.51185 65.11333
8.00 48.00000 38.83282 38.83282 48.00000 56.42738 33.69007 28.33997 32.59744 19.02887 31.15380 58.84620 46.67124 54.53638 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 21.95009 29.27927 63.37054
9.00 48.00000 38.83282 38.83282 48.00000 56.42738 36.86990 31.24782 31.84624 20.65078 30.16661 59.83339 48.54102 56.14484 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 23.55362 28.04911 61.55508
10.00 48.00000 38.83282 38.83282 48.00000 56.42738 39.80557 33.98709 31.06571 22.10412 29.16787 60.83213 50.54900 57.88967 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 24.94414 26.84312 59.69977
11.00 48.00000 38.83282 38.83282 48.00000 56.42738 42.51045 36.56059 30.26693 23.40207 28.17234 61.82766 52.67937 59.75892 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 26.14839 25.67643 57.83237
12.00 48.00000 38.83282 38.83282 48.00000 56.42738 45.00000 38.97345 29.45956 24.55880 27.19152 62.80848 54.91789 61.74130 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 27.19152 24.55880 55.97550
13.00 48.00000 38.83282 38.83282 48.00000 56.42738 47.29061 41.23246 28.65176 25.58862 26.23405 63.76595 57.25189 63.82626 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 28.09624 23.49587 54.14700
14.00 48.00000 38.83282 38.83282 48.00000 56.42738 49.39871 43.34551 27.85027 26.50525 25.30608 64.69392 59.67015 66.00408 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 28.88254 22.49021 52.36040
15.00 48.00000 38.83282 38.83282 48.00000 56.42738 51.34019 45.32108 27.06049 27.32151 24.41175 65.58825 62.16284 68.26588 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 29.56773 21.54221 50.62558
16.00 48.00000 38.83282 38.83282 48.00000 56.42738 53.13010 47.16791 26.28668 28.04911 23.55362 66.44638 64.72136 70.60359 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 30.16661 20.65078 48.94935
17.00 48.00000 38.83282 38.83282 48.00000 56.42738 54.78241 48.89470 25.53202 28.69857 22.73295 67.26705 67.33821 73.00991 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 30.69175 19.81388 47.33604
18.00 48.00000 38.83282 38.83282 48.00000 56.42738 56.30993 50.50993 24.79886 29.27927 21.95009 68.04991 70.00685 75.47829 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 31.15380 19.02887 45.78800
19.00 48.00000 38.83282 38.83282 48.00000 56.42738 57.72436 52.02175 24.08879 29.79947 21.20469 68.79531 72.72158 78.00283 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 31.56173 18.29280 44.30609
20.00 48.00000 38.83282 38.83282 48.00000 56.42738 59.03624 53.43786 23.40283 30.26643 20.49590 69.50410 75.47743 80.57825 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 31.92312 17.60259 42.88999
21.00 48.00000 38.83282 38.83282 48.00000 56.42738 60.25512 54.76550 22.74148 30.68651 19.82251 70.17749 78.27004 83.19983 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 32.24437 16.95516 41.53855
22.00 48.00000 38.83282 38.83282 48.00000 56.42738 61.38954 56.01141 22.10490 31.06526 19.18311 70.81689 81.09563 85.86334 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 32.53089 16.34749 40.25000
23.00 48.00000 38.83282 38.83282 48.00000 56.42738 62.44719 57.18183 21.49292 31.40751 18.57615 71.42385 83.95086 88.56500 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 32.78727 15.77673 39.02219
24.00 48.00000 38.83282 38.83282 48.00000 56.42738 63.43495 58.28253 20.90516 31.71747 18.00000 72.00000 86.83282 91.30143 77.66563 56.42738 72.00000 17.43702 18.00000 53.66563 301.59289 33.01740 15.24016 37.85264
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 = 54.00000
Roof Surface Angle C Bay # 0 = 72.00000
Roof Surface Angle B Bay # 0 = 54.00000

Roof Surface Angle A Bay # 1 = 54.09423
Roof Surface Angle C Bay # 1 = 71.81155
Roof Surface Angle B Bay # 1 = 54.09423

Roof Surface Angle A Bay # 2 = 54.37245
Roof Surface Angle C Bay # 2 = 71.25509
Roof Surface Angle B Bay # 2 = 54.37245

Roof Surface Angle A Bay # 3 = 54.82191
Roof Surface Angle C Bay # 3 = 70.35617
Roof Surface Angle B Bay # 3 = 54.82191

Roof Surface Angle A Bay # 4 = 55.42311
Roof Surface Angle C Bay # 4 = 69.15379
Roof Surface Angle B Bay # 4 = 55.42311

Roof Surface Angle A Bay # 5 = 56.15204
Roof Surface Angle C Bay # 5 = 67.69593
Roof Surface Angle B Bay # 5 = 56.15204

Roof Surface Angle A Bay # 6 = 56.98260
Roof Surface Angle C Bay # 6 = 66.03480
Roof Surface Angle B Bay # 6 = 56.98260

Roof Surface Angle A Bay # 7 = 57.88876
Roof Surface Angle C Bay # 7 = 64.22247
Roof Surface Angle B Bay # 7 = 57.88876

Roof Surface Angle A Bay # 8 = 58.84620
Roof Surface Angle C Bay # 8 = 62.30760
Roof Surface Angle B Bay # 8 = 58.84620

Roof Surface Angle A Bay # 9 = 59.83339
Roof Surface Angle C Bay # 9 = 60.33322
Roof Surface Angle B Bay # 9 = 59.83339

Roof Surface Angle A Bay # 10 = 60.83213
Roof Surface Angle C Bay # 10 = 58.33574
Roof Surface Angle B Bay # 10 = 60.83213

Roof Surface Angle A Bay # 11 = 61.82766
Roof Surface Angle C Bay # 11 = 56.34467
Roof Surface Angle B Bay # 11 = 61.82766

Roof Surface Angle A Bay # 12 = 62.80848
Roof Surface Angle C Bay # 12 = 54.38304
Roof Surface Angle B Bay # 12 = 62.80848

Roof Surface Angle A Bay # 13 = 63.76595
Roof Surface Angle C Bay # 13 = 52.46810
Roof Surface Angle B Bay # 13 = 63.76595

Roof Surface Angle A Bay # 14 = 64.69392
Roof Surface Angle C Bay # 14 = 50.61215
Roof Surface Angle B Bay # 14 = 64.69392

Roof Surface Angle A Bay # 15 = 65.58825
Roof Surface Angle C Bay # 15 = 48.82351
Roof Surface Angle B Bay # 15 = 65.58825

Roof Surface Angle A Bay # 16 = 66.44638
Roof Surface Angle C Bay # 16 = 47.10723
Roof Surface Angle B Bay # 16 = 66.44638

Roof Surface Angle A Bay # 17 = 67.26705
Roof Surface Angle C Bay # 17 = 45.46589
Roof Surface Angle B Bay # 17 = 67.26705

Roof Surface Angle A Bay # 18 = 68.04991
Roof Surface Angle C Bay # 18 = 43.90018
Roof Surface Angle B Bay # 18 = 68.04991

Roof Surface Angle A Bay # 19 = 68.79531
Roof Surface Angle C Bay # 19 = 42.40938
Roof Surface Angle B Bay # 19 = 68.79531

Roof Surface Angle A Bay # 20 = 69.50410
Roof Surface Angle C Bay # 20 = 40.99179
Roof Surface Angle B Bay # 20 = 69.50410

Roof Surface Angle A Bay # 21 = 70.17749
Roof Surface Angle C Bay # 21 = 39.64502
Roof Surface Angle B Bay # 21 = 70.17749

Roof Surface Angle A Bay # 22 = 70.81689
Roof Surface Angle C Bay # 22 = 38.36623
Roof Surface Angle B Bay # 22 = 70.81689

Roof Surface Angle A Bay # 23 = 71.42385
Roof Surface Angle C Bay # 23 = 37.15230
Roof Surface Angle B Bay # 23 = 71.42385

Roof Surface Angle A Bay # 24 = 72.00000
Roof Surface Angle C Bay # 24 = 36.00000
Roof Surface Angle B Bay # 24 = 72.00000