Last save: 2019-02-27 60 Seconds animation on: https://ero.ossel.nl/index.php/a-homepage-section/penthouse/ History Started long time ago, around 2005, with a little Icosahedron or Dodecahedron dome house. Then came the question having a stair along the walls, the faces of the Polyhedral, what is its angle. Ended up with the stair on level 3, the stair-halves have an angle of 120 degrees. Interesting was dealing with one halve along a wall pointing inside and the other halve along a wall pointing outside. It is at the end a little bigger than expected, and for the static an Icosahedron as a centre, bearing up the Dodecahedron. An optimal scale is 77 step rises of 0.17 meter between the planes of floor 3 and 6. With the given 0.17 step rise, the formula step length of 0.63 meter = 2 x rises + 1 x going brings a step going of 0.29 meter: 0.63-(2*0.17)=0.29. Because I’m a European, grown up with the metric system, the measurements are in meters. Some puzzling with a free standing elevator and chimney; afterwards came the ramp to level 1. This one is that expensive in render time, defined by a lot of small cylinders, I quit further development and started to render the 60 seconds animations. 18 Months later is here the result: ErO’s Penthouse. Levels All levels ID Up Plane Down Flt Rises Height Description 9 19.89 19.675 19.38 Sky DH 0 8 14.96 14.665 14.45 3 26 4.42 Roof DH 1,4,19 7 10.88 10.605 10.54 2 21 3.57 Flat two mid of level 8 and level 6 6 6.80 6.545 6.29 3 22 3.74 Flat one mid of DH 2,3,5,11,12,18 and IH 3,4,5 5 1.70 1.542 1.36 2 27 4.59 Mid High IH 0,9,10 4 -1.36 -1.542 -1.70 2 16 2.72 Mid Low IH 2,8,11 3 -6.29 -6.545 -6.80 3 27 4.59 Entrance mid of IH 1,6,7 and DH 6,7,9,10,13,17 2 -10.54 -10.605 -10.88 2 22 3.74 Nessi mid of level 3 and level 1 1 -14.45 -14.665 -14.96 3 21 3.57 Basement DH 8,14,16 0 -19.38 -19.675 -19.89 3 26 4.42 Catacombs DH 15 Up = upside of floor, relative to Point Zero Plane = position inside floor, calculated on the nodes of Dodecahedron and Icosahedron Down = downside of floor, relative to Point Zero … (is ceiling room underneath, L0 and L9 are fictive) Flt = floor thickness in number of step rises Rises = amount of step rises Height = difference between floor and ceiling in meters Top of granite pillar of level 0 is on the first step, the actual floor of 3 rises is not rendered Top of Penthouse (Level 9) is rendered without floor. The image shows the Dodecahedron a little bit “floating” above the granite pillar/fundament. With respect to the diameter vertices, the lowest point of node “a_DH_Node[15]” is one step side inside the granite pillar.. 9: Sky Level 9: Sky There is no stairway to heaven 8: Roof Level 8: Roof Top-terrace, a round floor like in animation Dome, will gives much more place. 7: Flat two Level 7: Flat two Upper-“Penthouse”, the bay window is here for keeping 2.5 m above stair, in Dome not needed, but with the diagonals you will have a problem with the door on this side of the elevator . 6: Flat one Level 6: Flat one Lower-“Penthouse” 5: Mid High Level 5: Mid High Central ceiling with cut-out (≈ half of floor thickness) of Icosahedron 4: Mid Low Level 4: Mid Low Lowest room with a height of 2.72 m and a bridge, keeping 2.5 m headroom. Central cut-outs are the shape of the Icosahedron, build on the conversation pit of level 3. 3: Entrance Level 3: Entrance Ground level, with conversation pit, base of Icosahedron. 2: Nessi Level 2: Nessi Fitness and Wellness, for my wife left fitness, for me at the right wellness with pub Nessi. 1: Basement Level 1: Basement Parking 0: Catacombs Level 0: Catacombs SM Studios Frame & Fundament Frame & Fundament Frame outside: a Dodecahedron; frame inside: a “Tensegrity Icosahedron” Dome ErO's Dome Skeleton · Length 12*5 Cyan struts: 14.06 meter · Length 2*3 Blue, Green & Red struts: 13.98 meter The skeleton, bridging construction, between the nodes of Dodecahedron and Icosahedron and the struts inside the “Tensegrity Icosahedron”. Dodecahedron Dodecahedron numbered · Circumsphere: 19,67 meter · Length edge: 14.04 meter · Radius edge: 0.2188040502 meter · Length diagonal Pentagon: 22.72 meter · Radius diagonal Pentagon: 0.05 meter · In the three lowest Pentagons, level 0, 1 & 2, are the diagonals not present, therefor additional fundament. a_DH_Node[ 0]: < -0.000000, 19.674750, -0.000000> a_DH_Node[ 1]: <-11.359222, 14.664693, 6.558250> a_DH_Node[ 2]: <-18.379607, 6.558250, -2.505029> a_DH_Node[ 3]: <-11.359222, 6.558250,-14.664693> a_DH_Node[ 4]: < 0.000000, 14.664693,-13.116500> a_DH_Node[ 5]: < 11.359222, 6.558250,-14.664693> a_DH_Node[ 6]: < 7.020385, -6.558250,-17.169721> a_DH_Node[ 7]: < -7.020385, -6.558250,-17.169721> a_DH_Node[ 8]: <-11.359222,-14.664693, -6.558250> a_DH_Node[ 9]: <-18.379607, -6.558250, 2.505029> a_DH_Node[10]: <-11.359222, -6.558250, 14.664693> a_DH_Node[11]: < -7.020385, 6.558250, 17.169721> a_DH_Node[12]: < 7.020385, 6.558250, 17.169721> a_DH_Node[13]: < 11.359222, -6.558250, 14.664693> a_DH_Node[14]: < -0.000000,-14.664693, 13.116500> a_DH_Node[15]: < 0.000000,-19.674750, 0.000000> a_DH_Node[16]: < 11.359222,-14.664693, -6.558250> a_DH_Node[17]: < 18.379607, -6.558250, 2.505029> a_DH_Node[18]: < 18.379607, 6.558250, -2.505029> a_DH_Node[19]: < 11.359222, 14.664693, 6.558250> Distance between neighbor nodes of Dodecahedron is 14.04 meter. Icosahedron Tensegrity Icosahedron numbered · Circumsphere: 8.22 meter · Length edge: 8.64 meter · Radius edge: 0.10 meter · Length struts: 13.98 meter · Radius struts: 0.20 meter a_IH_Node[ 0]: < 6.992018, 1.541937, 4.036844> a_IH_Node[ 1]: < 4.321305,-6.531750, 2.494907> a_IH_Node[ 2]: <-6.992018,-1.541937,-4.036844> a_IH_Node[ 3]: <-4.321305, 6.531750,-2.494907> a_IH_Node[ 4]: < 4.321305, 6.531750,-2.494907> a_IH_Node[ 5]: <-0.000000, 6.531750, 4.989813> a_IH_Node[ 6]: <-4.321305,-6.531750, 2.494907> a_IH_Node[ 7]: < 0.000000,-6.531750,-4.989813> a_IH_Node[ 8]: < 6.992018,-1.541937,-4.036844> a_IH_Node[ 9]: < 0.000000, 1.541937,-8.073687> a_IH_Node[10]: <-6.992018, 1.541937, 4.036844> a_IH_Node[11]: <-0.000000,-1.541937, 8.073687> It’s a “Tensegrity Icosahedron”: https://en.wikipedia.org/wiki/Tensegrity#Tensegrity_Icosahedra. The 2 times 3 colored struts (Blue, Green and Red) between floors 3 and 5 and between floors 4 and 6 represents the 12 nodes of Icosahedron. The 6 vertices between the same colored struts are missing. Distance between neighbor nodes of Icosahedron is 8.64 meter. Stairs Stair level 3 · Step rise: 0.17 meter (exception conversation pit in floor 3: 0.15 meter) · Step going: 0.29 meter (exception conversation pit in floor 3: 0.33 meter) · Formula: 2 x rise + going = 0.63 meter · Width (mostly): 2.00 meter Level 0: width = 1.30 meter Level 7: width = 1.10 meter Level Object Step rises Total 8 Floor 3 24 Room 19 2 7 Floor 2 24 Room 8 14 6 Floor 3 30 Room 13 14 5 Floor 2 18 Room 16 4 Floor 2 29 Room 16 11 3 Floor 3 25 Room 6 16 2 Floor 2 23 Room 8 7 6 1 Floor 3 Room 12 9 5 31 0 2 “Floor” 1 N/A Floor 0 is not really there; height is part of the underground and room (Catacombs). Floors Level 3, inside Squared grid is 2 by 2 meters. · Floor level 0: lowest step rise is in the underground, and the upper two step rises are part of the room. · If node of Dodecahedron is present it has three step rises, other floors are two step rises. Floor 4 and 5 has only nodes of Icosahedron, also two step rises! · Note the little difference in height of the DodecaHedron-nodes and IcosaHedron-nodes in floor 3 and 6: heights of IH (= ±6.531750) & DH (= ±6.558250) gives a middle for the floors of 3 & 6 on ±6.545000, total rises of stairs on level 3,4 & 5 = 29+18+30 = 77, delightful…, exactly 77*0.17 = 6.545*2. · Floor of level 9 is top of Dodecahedron, no floor, no “Stairway to Heaven”. Baffles · Standard height is 2.5 meter and has a variable width. · Exception: left of stair going down to level 2 on floor 3! Below a tube: warning: mind your head Above a tube: info: watch your feet (most of these are when tube is pointing outside) 4 Cardinal directions Blue: East, Yellow: South, Red: West and Black: North For orientation are the 4 pillars (Blue: East, Yellow: South, Red: West and Black: North) Bugs Bug with short railing (vertical tubes are missing) on pedestal · Rendered on: o All levels o Level 0 o Level 2 o Level 4 with axis o Level 6 · Involved stairs on: o Floor 7 o Floor 6 o Floor 5 o Floor 3 o Floor 1 o Floor 0 The first, and maybe last, step top should be a 0.00001 higher, it is on the same height as floor, and might causing a flickering in animation.