Developmental Geometry for a Pyramid with an (6 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 | 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°