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 . Then came the question having a stair along the , 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 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 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 and ; 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 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 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 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-, a round floor like in animation Dome, will gives much more place. 7: Flat two

Level 7: Flat two

Upper-“Penthouse”, the bay is here for keeping 2.5 m above stair, in Dome not needed, but with the diagonals you will have a problem with the 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 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 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.

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.