Developmental Geometry for a Pyramid with an (24 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 15
working angle = 7.5
plan angle = 82.5
miter angle = 1.58 & 12
hip run per foot = 12.1035475269618
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.00862896058015
side_wall_multiplier = 0.263304995174792
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 47.58935 47.58935 48.00000 12.53051 0.00000 0.00000 7.50000 0.00000 7.50000 82.50000 47.58935 48.00000 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 0.00000 7.50000 15.00000
1.00 48.00000 47.58935 47.58935 48.00000 12.53051 4.76364 4.72307 7.47482 0.62108 7.47439 82.52561 47.75431 48.16355 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 0.62640 7.47394 14.94906
2.00 48.00000 47.58935 47.58935 48.00000 12.53051 9.46232 9.38282 7.40078 1.22957 7.39909 82.60091 48.24579 48.65090 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 1.23989 7.39738 14.79932
3.00 48.00000 47.58935 47.58935 48.00000 12.53051 14.03624 13.92085 7.28212 1.81413 7.27851 82.72149 49.05398 49.45247 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 1.82886 7.27484 14.55943
4.00 48.00000 47.58935 47.58935 48.00000 12.53051 18.43495 18.28777 7.12519 2.36561 7.11918 82.88082 50.16358 50.55332 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 2.38397 7.11308 14.24239
5.00 48.00000 47.58935 47.58935 48.00000 12.53051 22.61986 22.44562 6.93758 2.87759 6.92892 83.07108 51.55513 51.93443 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 2.89873 6.92014 13.86363
6.00 48.00000 47.58935 47.58935 48.00000 12.53051 26.56505 26.36865 6.72722 3.34643 6.71586 83.28414 53.20651 53.57412 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 3.36950 6.70435 13.43932
7.00 48.00000 47.58935 47.58935 48.00000 12.53051 30.25644 30.04263 6.50168 3.77097 6.48773 83.51227 55.09437 55.44946 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 3.79521 6.47362 12.98480
8.00 48.00000 47.58935 47.58935 48.00000 12.53051 33.69007 33.46324 6.26766 4.15201 6.25134 83.74866 57.19528 57.53741 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 4.17676 6.23487 12.51360
9.00 48.00000 47.58935 47.58935 48.00000 12.53051 36.86990 36.63389 6.03073 4.49176 6.01234 83.98766 59.48669 59.81572 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 4.51650 5.99381 12.03697
10.00 48.00000 47.58935 47.58935 48.00000 12.53051 39.80557 39.56366 5.79529 4.79327 5.77516 84.22484 61.94746 62.26348 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 4.81761 5.75489 11.56376
11.00 48.00000 47.58935 47.58935 48.00000 12.53051 42.51045 42.26533 5.56464 5.06005 5.54309 84.45691 64.55821 64.86152 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 5.08370 5.52142 11.10057
12.00 48.00000 47.58935 47.58935 48.00000 12.53051 45.00000 44.75386 5.34114 5.29571 5.31847 84.68153 67.30151 67.59250 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 5.31847 5.29571 10.65207
13.00 48.00000 47.58935 47.58935 48.00000 12.53051 47.29061 47.04517 5.12633 5.50376 5.10282 84.89718 70.16180 70.44098 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 5.52553 5.07924 10.22132
14.00 48.00000 47.58935 47.58935 48.00000 12.53051 49.39871 49.15530 4.92115 5.68751 4.89705 85.10295 73.12536 73.39327 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 5.70821 4.87288 9.81016
15.00 48.00000 47.58935 47.58935 48.00000 12.53051 51.34019 51.09983 4.72608 5.84996 4.70158 85.29842 76.18014 76.43734 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 5.86958 4.67704 9.41948
16.00 48.00000 47.58935 47.58935 48.00000 12.53051 53.13010 52.89353 4.54122 5.99381 4.51650 85.48350 79.31559 79.56266 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.01234 4.49176 9.04947
17.00 48.00000 47.58935 47.58935 48.00000 12.53051 54.78241 54.55015 4.36647 6.12141 4.34167 85.65833 82.52252 82.76002 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.13890 4.31687 8.69985
18.00 48.00000 47.58935 47.58935 48.00000 12.53051 56.30993 56.08235 4.20153 6.23487 4.17676 85.82324 85.79293 86.02139 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.25134 4.15201 8.37001
19.00 48.00000 47.58935 47.58935 48.00000 12.53051 57.72436 57.50169 4.04600 6.33598 4.02136 85.97864 89.11981 89.33977 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.35149 3.99676 8.05912
20.00 48.00000 47.58935 47.58935 48.00000 12.53051 59.03624 58.81862 3.89942 6.42631 3.87499 86.12501 92.49708 92.70902 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.44091 3.85061 7.76623
21.00 48.00000 47.58935 47.58935 48.00000 12.53051 60.25512 60.04260 3.76130 6.50722 3.73713 86.26287 95.91941 96.12381 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.52097 3.71302 7.49034
22.00 48.00000 47.58935 47.58935 48.00000 12.53051 61.38954 61.18211 3.63113 6.57988 3.60727 86.39273 99.38215 99.57944 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.59283 3.58348 7.23041
23.00 48.00000 47.58935 47.58935 48.00000 12.53051 62.44719 62.24481 3.50841 6.64530 3.48489 86.51511 102.88122 103.07181 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.65750 3.46145 6.98542
24.00 48.00000 47.58935 47.58935 48.00000 12.53051 63.43495 63.23753 3.39265 6.70435 3.36950 86.63050 106.41303 106.59731 95.17871 12.53051 15.00000 12.10355 75.00000 3.24314 301.59289 6.71586 3.34643 6.75439
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 = 82.50000
Roof Surface Angle C Bay # 0 = 15.00000
Roof Surface Angle B Bay # 0 = 82.50000

Roof Surface Angle A Bay # 1 = 82.52561
Roof Surface Angle C Bay # 1 = 14.94877
Roof Surface Angle B Bay # 1 = 82.52561

Roof Surface Angle A Bay # 2 = 82.60091
Roof Surface Angle C Bay # 2 = 14.79819
Roof Surface Angle B Bay # 2 = 82.60091

Roof Surface Angle A Bay # 3 = 82.72149
Roof Surface Angle C Bay # 3 = 14.55701
Roof Surface Angle B Bay # 3 = 82.72149

Roof Surface Angle A Bay # 4 = 82.88082
Roof Surface Angle C Bay # 4 = 14.23836
Roof Surface Angle B Bay # 4 = 82.88082

Roof Surface Angle A Bay # 5 = 83.07108
Roof Surface Angle C Bay # 5 = 13.85783
Roof Surface Angle B Bay # 5 = 83.07108

Roof Surface Angle A Bay # 6 = 83.28414
Roof Surface Angle C Bay # 6 = 13.43171
Roof Surface Angle B Bay # 6 = 83.28414

Roof Surface Angle A Bay # 7 = 83.51227
Roof Surface Angle C Bay # 7 = 12.97546
Roof Surface Angle B Bay # 7 = 83.51227

Roof Surface Angle A Bay # 8 = 83.74866
Roof Surface Angle C Bay # 8 = 12.50268
Roof Surface Angle B Bay # 8 = 83.74866

Roof Surface Angle A Bay # 9 = 83.98766
Roof Surface Angle C Bay # 9 = 12.02468
Roof Surface Angle B Bay # 9 = 83.98766

Roof Surface Angle A Bay # 10 = 84.22484
Roof Surface Angle C Bay # 10 = 11.55031
Roof Surface Angle B Bay # 10 = 84.22484

Roof Surface Angle A Bay # 11 = 84.45691
Roof Surface Angle C Bay # 11 = 11.08619
Roof Surface Angle B Bay # 11 = 84.45691

Roof Surface Angle A Bay # 12 = 84.68153
Roof Surface Angle C Bay # 12 = 10.63694
Roof Surface Angle B Bay # 12 = 84.68153

Roof Surface Angle A Bay # 13 = 84.89718
Roof Surface Angle C Bay # 13 = 10.20564
Roof Surface Angle B Bay # 13 = 84.89718

Roof Surface Angle A Bay # 14 = 85.10295
Roof Surface Angle C Bay # 14 = 9.79409
Roof Surface Angle B Bay # 14 = 85.10295

Roof Surface Angle A Bay # 15 = 85.29842
Roof Surface Angle C Bay # 15 = 9.40315
Roof Surface Angle B Bay # 15 = 85.29842

Roof Surface Angle A Bay # 16 = 85.48350
Roof Surface Angle C Bay # 16 = 9.03300
Roof Surface Angle B Bay # 16 = 85.48350

Roof Surface Angle A Bay # 17 = 85.65833
Roof Surface Angle C Bay # 17 = 8.68334
Roof Surface Angle B Bay # 17 = 85.65833

Roof Surface Angle A Bay # 18 = 85.82324
Roof Surface Angle C Bay # 18 = 8.35353
Roof Surface Angle B Bay # 18 = 85.82324

Roof Surface Angle A Bay # 19 = 85.97864
Roof Surface Angle C Bay # 19 = 8.04273
Roof Surface Angle B Bay # 19 = 85.97864

Roof Surface Angle A Bay # 20 = 86.12501
Roof Surface Angle C Bay # 20 = 7.74998
Roof Surface Angle B Bay # 20 = 86.12501

Roof Surface Angle A Bay # 21 = 86.26287
Roof Surface Angle C Bay # 21 = 7.47427
Roof Surface Angle B Bay # 21 = 86.26287

Roof Surface Angle A Bay # 22 = 86.39273
Roof Surface Angle C Bay # 22 = 7.21454
Roof Surface Angle B Bay # 22 = 86.39273

Roof Surface Angle A Bay # 23 = 86.51511
Roof Surface Angle C Bay # 23 = 6.96979
Roof Surface Angle B Bay # 23 = 86.51511

Roof Surface Angle A Bay # 24 = 86.63050
Roof Surface Angle C Bay # 24 = 6.73900
Roof Surface Angle B Bay # 24 = 86.63050