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. Same for landing of pedestal between two stairs, landing should be 0.000001 wider.
Stair on level 3 (left-turning up) is missing the vertical tubes on the bends of pedestal, corrected between 156.80 (1466) .. 90.20 (1799) during render L4. Renders AL, L0, L1, L2, L4 with axis, L6, L8. Visible in AL, L2, L4 with axis, L4 except between 90.20 and 156.80.
Something wrong with Nessie left slide-door when looking outside.