Scroll down below these basic geometries to see the listings within this original chart.
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Start in the centerleft column below. All units of measurement are based on the Planck Length. On the left going down the numbers are divided 101 times by two until the measurement is the Planck Length, considered the smallest unit of a length. In the centerright column, the same measurement is multiplied by two. In 101+ steps we are out to the edges of the observable universe. Assume the simplest threedimensional form defined by the fewest number of vertices is the tetrahedron. Notice how the the basic Platonic structures nest within each other. Necessarily all structure of every manifestation within the known universe can be interrelated. There are blanks for students to find answers from examples within their studies, especially biology, chemistry, physics, astronomy and astrophysics. Students are also invited to correct mistakes. Basic Questions and Structures, and FormandFunction: Could all structures be in some way derivative of the five basic solids discussed by Plato and the Greeks (circa 360 BC)? If that concept is taken as a given, then questions about form and function can be reengaged. Perhaps base2 exponential notation is a place to start. Though apparent throughout the sciences, these five basic solids have not been used to develop an integrative model for human knowledge. Perhaps this is a step in that direction. Most academics today cannot tell you what is most simply contained within a tetrahedron or octahedron (by dividing the edges in half and connecting the vertices). Pictures below illustrate some answers. It seems that simple mathematical operations can still open new paths and logic to explore. More… 

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GENERAL DISCIPLINES (and Scale) 
PLANCK NUMBER. EXAMPLES (within ±50%) 
DECREASING IN SIZE, Get smaller, divide by 2 (Center left column)  ___ 
INCREASING IN SIZE, Get larger, Multiply by 2 (Center right column)

PLANCK NUMBER. EXAMPLES
(within ±50%) 
GENERAL DISCIPLINES (and Scale) 
HUMAN SCALE  101. Range: Human Hair  40.9755356 microns  ___  Around 40 microns  101. Thicker Hair  HUMAN SCALE 
BIOLOGY  100. Sperm cell diameter  20.4877678 microns  81.9510712 microns  102. Thickness of paper  MANUFACTURING  
Cytology  99. Diameter of average human body cells  10.2438839 microns or 1.02438839×10^{5}m 
.163902142 millimeters or 1.63902142×10^{4}m 
103. Egg cell diameter  ___  
Microbiology  98. Diameter of average human capillary  5.12194196 microns or about .0002 inches 
.327804284 millimeters  104. This period. Got it?  ___  
97. Red blood cells~2.4 µm  2.56097098 microns (µm)  .655608568 millimeters  105. Large bacterium  Bacteriology  
Bacteriology  96. Rather small bacteria and red light (1.28 µm)  1.28048549 microns or 1.2804854×10^{6} m  1.31121714 millimeters or 1.3112171×10^{3}m  106. Large grain of sand  ___  
Nanotechnology  95. Range of visible light ~ 400 to 1000 nm  640.242744 nanometers  2.62243428 millimeters  107. A small ant  Myrmecology  
___  94. Nanoparticles ~ 10000 to 100 nm  320.121372 nanometers  5.24486856 millimeters (around a quarter inch)  108. Very small objects that we can still handle  PHYSICS  
___  93. Thickness of gold leaf ~125 nm  160.060686 nanometers  1.04897 centimeters or 1.04897375×10^{2}m  109. Often parts of common small objects  CHEMISTRY  
___  92. Nanowires  80.0303432 nanometers  2.09794742 centimeters  110. Rather small things  ELECTRONICS  
___  91. Semiconductor chip  40.0151716 nanometers  4.19589484 centimeters  111. A spoonful  TECHNOLOGY  
Virology  90. Virus range  20.0075858 nanometers  8.39178968 centimeters  112. Anything 3.3 inches!  BIOLOGY  
___  89. Thickness of a cell wall is around 10 nm  1.00037929×10^{8} meters or 10 nanometers  16.7835794 centimeters or 1.67835794×10^{1}m  113: Small living and manufactured things  ZOOLOGY  
Immunology  88. Insulin molecule  5.00189644×10^{–}^{9} meters  33.5671588 centimeters  114. Objects we handle  BOTANY  
___  87. DNA helix ±2 nm  2.50094822 nanometers  67.1343176 centimeters or 19.68 inches  115. Agricultural and manufactured things  ANTHROPOLOGY  
Chemistry  86. Glucose molecule Fullerenes diameter (Buckyballs) range: ~1.1nm  1.25474112 nanometers  1.3426864 meters or 52.86 inches  116. A child or other smaller animals  SLEEP & VISIONS  
Genetics  85. Distance between base pairs within DNA ±340 pm  .625237056 nanometers or 6.25237056×10^{10} meters  2.6853728 meters or 105.723 inches  117. A bed, a little stable or place to rest  INSIGHTS & IDEAS  
HUMAN SCALE PN 67 to 134 
84. Periodic Table is complete. Diameter of a water molecule ±280 pm  .312618528 nanometers or 3.12618528×10^{10} meters  5.3707456 meters  118. A small bedroom  PSYCHOLOGY  
Picometres pm 
83. Diameter of a carbon atom ±70 pm  .156309264 nanometers or 1.56309264×10^{10}m  10.7414912 meters, 35.2411 feet  119. A home, a small barn or shop  SOCIOLOGY  
___  82. Helium atom diameter  7.81546348×10^{11} meters  .  21.4829824 meters  120. Property  FAMILIES 
___  81. Hydrogen atom ±25 pm  3.90773174×10^{11} meters  42.9659648 meters  121. Larger properties  RETAIL  
___  80. Periodic Table of Elements begins  1.95386587×10^{11}m  85.9319296 meters  122. Complex systems  CONSTRUCTION  
___  79. Use Huang scale  9.76932936×10^{12}m  171.86386 meters or about 563 feet  123. Big buildings or a little neighborhood  GEOLOGY  
___  78. Wavelength of an Xray  4.88466468×10^{12}m  343.72772 meters or about 1128 feet  124. A huge complex or a neighborhood  ARCHITECTURE  
___  77.  2.44233234×10^{12} m  687.455439 meters  125. Farms and large complexes  AGRICULTURE  
___  76. Gamma wavelength  1.22116617×10^{12}m  1.37491087 kilometers  126. Very small towns  SMALL POLITICAL SYSTEMS  
BEGINNINGS OF  75. Use Falstad scale  6.10583084×10^{13}m  2.74982174 kilometers  127. Smallest states  TRANSPORTATION  
SMALL SCALE  74. ___  3.05291542×10^{13}m  5.49964348 kilometers  128. Towns  AERONAUTICS  
73.___  1.52645771×10^{13}m  10.999287 kilometers or within 6.83464 miles  129. Small cities, or large towns  JUDICIAL SYSTEMS  
NUCLEAR PHYSICS  72. Average range of the size of atom’s nucleus  7.63228856×10^{14}m  21.998574 kilometers  130. Large towns  LOCAL POLITICS  
___  71. Gold atomic nucleus  3.81614428×10^{14} m  43.997148 kilometers  131. Large cities  ___  
Human Scale  70. Aluminum atom  1.90807214×10^{14}m  87.994296 kilometers  132. Small states  ___  
Beginnings of  69. Electron diameter  9.54036072×10^{15}m  175.988592 kilometers or 108 miles  133. Very small countries or anything within 100 miles  NATIONAL POLITICS  
Going up  68. Helium atom diameter  4.77018036×10^{15} m  351.977184 kilometers or 218 miles  134. Within the orbital range: International Space Station  SPACE POLITICS  
Femtometres (fm)  67. Neutron diameter Hydrogen – 1.75±×10^{15}m  2.38509018×10^{15}m  703.954368 kilometers  135. Countries  BEGINNINGS OF  
Going down, beginnings of  66. Diameter of a proton or fermions (femtometre )  1.19254509×10^{15}m  1407.90874 kilometers or about 874 miles  136. Larger countries  LARGE SCALE  
small scale 
65. 36+ quintillion vertices  5.96272544×10^{16} m  2815.81748 kilometers  137. Regions of earth  ___  
THEORETICAL PHYSICS 
64. Neutrinos, quarks  2.98136272×10^{16}m  5631.63496 kilometers  138. Largest countries  ___  
Attometers  63. ___  1.49068136×10^{16}m  11,263.2699 kilometers or about 7000 miles  139. Diameter of the earth  ___  
am  62. ___  7.45340678×10^{17}m  22,526.5398 kilometers  140. GPS Satellite Altitude  ___  
61. ___  3.72670339×10^{17}m  45,053.079 kilometers  141. ___  ___  
VERYSMALL  60. 1+ quintillion vertices  1.86335169×10^{17}m  90,106.158 kilometers  142. ___  ___  
SCALE UNIVERSE  59. Quarks  9.31675848×10^{18}m  180,212.316 kilometers (over 111,979 miles)  143. ___  ___  
PN 40to60  58. ___  4.65837924×10^{18}m  360,424.632 kilometers  144. Distance: Earth to Moon  ___  
___  57. ___  2.32918962×10^{18}m  720,849.264 kilometers  145. ___  ___  
___  56. ___  1.16459481×10^{18}m  1,441,698.55 kilometers  146. Diameter of the sun  ___  
Zeptometers  55. ___  5.82297404×10^{–}^{19}m  2,883,397.1 kilometers  147. ___  ___  
zm  54. ___  2.91148702×10^{19}m  5,766,794.2 kilometers  148. ___  ___  
___  53. ___  1.45574351×10^{19}m  11,533,588.4 kilometers  149. ___  ___  
___  52. ___  7.27871756×10^{20}m  23,067,176.8 kilometers  150. ___  ___  
___  51. ___  3.63935878×10^{20}m  46,134,353.6 kilometers  151. ___  ___  
___  50. 1+ quadrillion vertices  1.81967939×10^{20}m  92,268,707.1 kilometers  152. ___  PN 134to201+  
___  49. ___  9.09839696×10^{21}m  184,537,414 kilometers  153. Range: Earth to Sun  ASTRONOMY  
___  48. ___  4.54919848×10^{21}m  369,074,829 kilometers  154. To go to Ceres asteroid  ___  
___  47. ___  2.27459924×10^{21}m  738,149,657 kilometers  155. Range: JupitertoSun  ___  
___  46. Pati Preons  1.13729962×10^{21}m  1.47629931×10^{12}m  156. Range: SaturntoSun  ASTROPHYSICS  
Yoctometers  45. ___  5.68649812×10^{–}^{22}m  2.95259863×10^{12}m  157.Range: UranustoSun  Terametres (Tm)  
ym  44. ___  2.84324906×10^{22}m  5.90519726×10^{12}m  158. Range: PlutotoSun  LARGE SCALE  
___  43. ___  1.42162453×10^{22}m  1.18103945×10^{13}m  159. ___  UNIVERSE  
___  42. ___  7.10812264×10^{23}m  2.36207882×10^{13}m  160. 24 hour light travel  ___  
___  41. THE CHALLENGE:  3.55406132×10^{23}m  4.72415764×10^{13}m  161. ___  ___  
VERYVERY,  40. 1+ trillion vertices  1.77703066×10^{23}m  9.44831528×10^{13}m  162. ___  ___  
SMALLSCALE  39. 549 billion vertices  8.88515328×10^{24}m  1.88966306×10^{14}m  163. 7day light travel  ___  
UNIVERSE  38. 274 billion vertices  4.44257664×10^{24}m  3.77932612×10^{14}m  164. ___  ___  
PN 20to40  37. 137 billion vertices  2.22128832×10^{24}m  7.55865224×10^{14}m  165. ___  ___  
36. 68 billion vertices  1.11064416×10^{24}m  1.5117305×10^{15}m  166. ___  Petametres (Pm)  
35. 34 billion vertices  5.5532208×10^{25}m  3.0234609×10^{15}m  167. ___  ___  
SPECULATIONS:  34. 17,179,869,184  2.7766104×10^{25}m  6.0469218×10^{15}m  168. ___  
Quantum State  33. 8,589,934,592  1.3883052×10^{25}m  1.20938436×10^{16}m  169. Beyond one light year (ly) (9.4×10^{15})  1 parsec ~ 31 trillion km or 19 trillion miles  
Machines (QSM)  32. 4,294,967,296  6.94152599×10^{26}m  2.41876872×10^{16}m  170. Go to Proxima Centauri (39.9 Pm)  1 parsec (3.26 light years, 30.8 Pm)  
(QSM)  31. 2,147,483,648  3.47076299×10^{26} m  4.83753744×10^{16}m  171. Distance to Alpha Centauri A & B (41 Pm)  ___  
___  30. 1+ billion vertices  1.735381494×10^{26} m  9.67507488×10^{16}m  172. Distance to Sirius (81 Pm, 8.6 ly)  ___  
Modulus for  29. 536,870,912  8.67690749×10^{27} m  1.93501504 ×10^{17}m  173. Distance to Tau Ceti (110 Pm)  100 Petametres or 11 light years (ly)  
transformations (Mt)  28. 268,435,456 b2v  4.3384537×10^{27}m  3.87002996×10^{17}m  174. Diameter of Orion Nebula (350 Pm)  ___  
27. 134,217,728 b2v  2.16922687×10^{27}m  7.74005992 ×10^{17}m  175. Distance to Regulus star (730 Pm)  ___  
Mt  26. 67,108,864 b2v  1.0846134×10^{27}m  1.54801198×10^{18}m  176. Omega Centauri diameter (1.6 Em)  Exametre (Em): 110 light years (ly)  
___  25. 33,554,432 b2v  5.42306718×10^{28} m  3.09602396×10^{18}m  177. Thickness of our Milky Way (2 Em)  Our Galaxy  
___  24. 16,777,216 b2 vertices  2.711533591×10^{28}m  6.19204792×10^{18}m  178. Distance to Helix Nebula (6.2 Em)  ___  
___  23. 8,388,608 b2 vertices  1.35576679×10^{28}m 1 barn 
1.23840958×10^{19}m  179. Distance to the Orion Nebula (13 Em)  12.38 Em  
QSM  22. 4,194,304 b2 vertices  6.77883397×10^{29}m  2.47681916×10^{19}m  180. Horsehead Nebula (15 Em)  ___  
___  21. 2,097,152 b2 vertices  3.38941698×10^{29}m  4.95363832×10^{19}m  181. ___  ___  
EXTREMELY  20. 1+ quintillion b8 vertices  1.69470849×10^{29}m  9.90727664×10^{19}m  182. ___  ___  
SMALLSCALE  19. 524,288 vertices  8.47354247×10^{30}m  1.981455338×10^{20}m  183. Small Megellanic Cloud diameter in Milky Way (150 Em)  198.1 Exametres  
UNIVERSE  18. 262,144 b2 vertices  4.2367712×10^{30}m  3.96291068×10^{20}m  184. To the center of our galaxy (260 Em)  ___  
PN 10to20  17. 281+ trillion b8 vertices  2.11838561×10^{30}m  7.92582136×10^{20}m  185. ___  ___  
16. one square femtometer  1.05919280×10^{30}m  1.58516432×109^{21}m  186. Go to Large Magellanic Cloud  1.5 Zettametre: 150,000 ly  
15. 32,768 base2 vertices  5.29596404×10^{31}m  3.17032864×10^{21}m  187. Small Magellanic Cloud (2 Zm)  3 Zettametres: 310,000 ly  
14. 4+ trillion base8 v  2.64798202×10^{31}m  6.34065727×10^{21}m  188. ___  ___  
13. 8192 vertices  1.32399101×10^{31}m  1.26813145×10^{22}m  189. ___  ___  
Note: ThetaFushian functions  12. 68+ billion base8 v  6.6199550×10^{32}m  2.53626284×10^{22}m  190. Distance to the Andromeda Galaxy  24 Zm  
See: Models  11. 2048 base2 vertices  3.30997752×10^{32}m  5.07252568×10^{22}m  191. ___  ___  
SMALLESTSCALE UNIVERSE 
10. 1+ billion base8 v  1.65498876×10^{32}m  1.01450514×10^{23}m  192. (Fill in a blank)  101 Zettametres  
Cubicities  9. 512 base2 vertices  8.27494384×10^{33}m  2.02901033×10^{23}m  193. Go to Centaurus A Galaxy (140 Zm)  ___  
Primary QSM  8. 16+ million base8 v  4.1374719232×10^{33}m  4.05802056×10^{23}m  194. (Fill in a blank)  ___  
Primary Mt  7. 128 base2 vertices  2.0687359616×10^{33}m  8.11604112×10^{23}m  195. ___  ___  
Nested Geometries  6. 262,144 base8 v  1.03436798×10^{33}m  1.62320822×10^{24}m  196. ___  Yottametre (Ym)  
Primary cubicities  5. 32 base2 vertices  5.17183990×10^{34}m  3.24641644×10^{24}m  197. Length of the Great Wall (4.7 Ym)  ___  
Strings & Knots  4. 4096 base8 vertices  2.58591995×10^{34}m  6.49283305×10^{24}m  198. Distance (6.1 Ym) to Shapley Supercluster  ___  
Primary knots  3. 8 base2 vertices  1.29295997×10^{34}m  1.29856658×10^{25}m  199. Length of Sloan Great Wall (13.7 Ym)  12.98 Ym  
Cubicity or string  2. 64 base8 vertices (v)  6.46479988×10^{35}  2.59713316×10^{25}m  200.___  ___  
Primary String  1. 2 base2 vertices (v)  3.23239994×10^{35}  5.19426632×10^{25}m  201.___  ___  
The Planck Length  A vertex?  1.616199(97)x10^{35}m  1.03885326×10^{26}m  202. EOU at 202.34  ___  
Synopsis: This Big Boardlittle universe is to order data in a way to open a discussion about our basic assumptions — the universals and constants — that guide our thinking and work. An initial focus is Max Planck’s calculation in 1900 of the Planck Length.
Very Brief History: The work began by attempting to find new starting points for creative thinking, new insights, even breakthroughs, regarding the very nature of space and time. In the 1970s the following first principles were formulated as preconditions for a spacetime moment at the zeropoint defined by Planck, Stern and Einstein. First principles: Deep within the fabric of life there is an energy, an abiding thrust to make things better, more perfect. That is the cornerstone of business, but much more. Simple logic tells us that there are three forms within functions that define an increasingly perfected state within an experience: These three — continuity, symmetry and harmony — just might be the precursors of a spacetime moment. 

A Working Project: A Big Board of our little universe This work is copyright by three groups, all of River Ridge, PO Box 10132 New Orleans, LA 70123 USA 
Illustration 3. Pentakis dodecahedron 32 external vertices or points, 60 external tetrahedra, a layer of 46 asymmetrical tetrahedral and an icosahedron in the center. 1.5° deviationsIllustration 2. Icosahedron 20 tetrahedrons made of 13 points, 1.5° deviations with shared center point 
The challenge of four simple concepts: 1. A universal scale created by doublings. A simple scale that starts with a point at the Planck Length (PL), assumes Planck’s logic and mathematics are OK and that the PL singularity, an actual measurement, can be doubled. At each step there is a physical measurement. It takes 202.34 doublings to go from the PL to the Edges of Observable Universe (EOU). See all of the above.2. Nested geometries. The first doubling renders two points and the second doubling four points. With four points a tetrahedron could be rendered; it is the simplest threedimensional form defined by the fewest number of points. The third doubling renders eight points. With just seven of those points, a pentagonal cluster of five tetrahedrons can be inscribed (Illustration 1). With the fourth doubling, now sixteen points, the icosahedron with its thirteen vertices (points) can be created. (Illustration 2). A tetrahedron within the pentagonal cluster (Illus. 1) can inscribe four smaller tetrahedra and an octahedron within itself with just six of those points (and by dividing each edge in half). More… 

This project was initiated for the geometry classes of Steve Curtis at The Curtis School, in River Ridge, Louisiana.Version 2.0.0.1 
Illustration 1. Five Tetrahedrons 7 points, 1.5° deviations 
3. Facts and Guesses. Simple math renders simple facts. What can be done with these numbers, images and forms? What functions can be intuited? Perhaps a challenge to students could be to use buckyballs and the basic Platonic solids to build a most primitive kind of machine. More to come…This quest is a thought experiment that begins at the PL and proceeds with facts and guesses to edge of the observable universe.4. Noncommutative geometry, irrational numbers… Another idiosyncratic application to number theory, noncommutative geometries, irrational numbers, and dimensionful numbers is to see all of these as the results of a modulus of transformation and gaps between faces of less than 1.5° (as seen in the sevenpoint, fiveregular tetrahedra when each shares an edge). Much more to come… 

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